That’s typical for what cyclists call the "angry monkey’ posture. Especially as you tire, there’s a tendency to bend your elbows out, let your head drop, and your spine curve. You can tell when someone is about to bonk on a hill, because they look like an angry monkey laboring on the bike. There’s a lot more core engagement on a bike than people expect.
Also check you have fit the bike to your body. I’m not sure how to properly fit a Peloton bike, but I know about road bikes. These are just basics, there are people who make a living fitting bikes. First, keep in mind everyone is shaped differently, so two people the same height with different torso/leg lengths won’t be able to share the same bike (or the same Peloton seat placement). For example, I wear a 37" shirt sleeve and a 34" inseam, so I am much more orangutan in proportions than other people my height (6’4"). Humans aren’t symmetrical either, but bikes are, so fine adjustments and shims can come into play if you are riding hard or far & need a perfect fit.
Step one is getting the correct frame size, but from looking at pictures online, it looks like Pelotons let you adjust that geometry. On road bikes, you want to look mostly at the length of the seat tube (which affects pedaling and saddle placement), and the length of the top tube (which affects reach, which dictates the angle of your back & pelvis). There are five contact points with a bike - hands, feet, and pelvis. If the frame is within a few inches of the correct placement of those, the other bike components and adjustments will get you to a comfortable, correct fit. For a Peloton, since you can adjust the critical geometry, fitting won’t involve buying new stems or moving the brake/shifter handles around (and re-taping the handlebars, ugh). Pedals may be an issue, I’ll cover that below.
Start fitting with saddle height, which is used to adjust the length of your pedal stroke. Where you like to put your feet on the pedals is a matter of preference, especially with cycling shoes on (they have incredibly stiff inserts built in, so they effectively lengthen the pedals front to back, giving you greater freedom in foot placement). From what I read, Pelotons require clip shoes, so foot placement may be solved. My feet splay out a bit, so I ride with the pedal spindle behind the ball of my big toe and in front of the ball of my pinkie toe (to find the angle of your feet, sit on a tall workbench or counter with a few inches of your thighs past the edge & relax your legs). Wherever your foot placement, your knee should be at 140-150 degrees at the bottom of the stroke, and your heel up about 10 degrees from level. Your knees need to stay in vertical line with your feet, so if your knees are angled in or out (top of the stroke is easiest to see this), then adjust your foot placement or your clips to get your feet directly under your knees. This is where Pelotons stray from my knowledge. SPD clips (short for Shimano Pedal Dynamics) and SPD-compatible pedals/shoes/clips dominate the market, but Peloton uses only Look’s Delta clips. I know many ways to adjust & shim SPD cleats & clips, but nothing about the Deltas (they’re plastic, which I think is why you don’t see Deltas on road bikes). I’ll assume they can be adjusted on Peloton’s shoes for foot placement and angle. If you have wide feet or naturally are heavily toes or heels in, you can buy spacers for road pedals to move the pedals farther from the cranks, or buy different pedals completely. Some thin washers of the correct internal and external diameter (deburred and given a thin coat of grease) can substitute for expensive alloy spacers, but I don’t know if there are aftermarket Peloton pedals. Look sells a wide variety of metal and ceramic pedals, almost all of which are SPD-compatible. Not sure why Peloton deviated from the industry standard here.
Next are the handlebars. Changing your hand contact points also affects your spine & pelvic angle, so adjust the height of the handlebar neck to change the angle of your back/pelvis. Higher will give you a straighter posture, but simultaneously decreases your reach. Peloton neck tubes look almost completely vertical, so reach won’t change much, they seem to rely on their saddle adjustment system for that. There are serious aerodynamic and steering disadvantages to high handlebars on road bikes, but those don’t matter here. Crank those things up like ape-hangers on a Harley if you need to, you have no worries about aero or steering. I’m not sure if Peloton lets you change the angle of the handlebars, but that’s something to look at if you want even more upright posture (for Zwift, I roll my drop handlebars toward myself until the drop ends are pointing up & 5-10 degrees past vertical, which gives me something to lean hard on when I get off the saddle for maximum power - I need to buy a tilt plate to truly stand & hammer on my trainer). But remember all of these angles affect each other, so you may need to adjust your saddle and clip placement. You may want to stick with certain grip areas on the Peloton bars to maintain posture.
When adjusting the handlebars, you don’t want to feel like you are reaching too far, that’s a sign you are straining your shoulders, spine, and pelvic angle. Neither do you want to feel cramped because the handlebars are too close. That usually will cause you to pull your elbows in or out and your shoulders up, putting you halfway to the Angry Monkey all of the time & almost certainly causing neck/shoulder pain. With that huge tube the saddle assembly slides on, reach adjustment looks very easy on a Peloton.
This isn’t related to neck or shoulder pain, but I don’t know if Peloton spends any time teaching muscle group engagement. “How to Pedal” should be lesson #1 in any exercise bike system. Your glutes should do most of the work when pedaling, closely followed by your hamstrings. Lots of people instead rely heavily on their quads, which will ruin your knees. It’s hard to describe a good pedalstroke form. It is mostly like you are stomping something with your heel, using your glutes & hammies to drive your fairly relaxed knee & everything below it down, but simultaneously keeping your feet relatively flat and moving them in little circles (not coincidentally, the diameter of your cranks). With clip pedals & rigid shoes, quads do more work than with flat pedals, but they shouldn’t be your main source of power. Quad-heavy cycling is guaranteed knee pain & injury. Quads & the smaller muscle groups in your lower legs stabilize your knees & feet, plus give you some power through the rest of the pedal circle, but glutes and hammies should be the kings. As you learn to isolate different muscle groups, you can become a distance god by alternating between them. My glutes and hammies will be screaming at the top of a hill or after a hard interval, but downhill or in the resting interval, that’s when you can alternate your calves and glutes under low stress & let the big guns rest. I’m lucky to have learned good form early in life (and been a nerd who avoided contact sports), because I have ridden hundreds of thousands of miles, I’m in my mid-50s, and my knees & hips don’t hurt.
Tl;dr: Sharp pain and persistent localized aches are bad, they are usually caused by improper bike fit, find the problem and fix it before they get worse.