The main guys were Thai SEALs and other Thai military who had trained with them. They had a medic and a doctor who went in to help the kids and stayed with them for some days. However, they stayed to help as far as I can tell, not because of oxygen problems.
@Matt_W has it right for the whole length of the caverns, but most only went partway in. Also while the rescue happened, there were additional helpers at each stop along the way to help apply doses, plus I think other divers took over carrying them for the last stages of the dive out well before they reached chamber 3.
As I understand it only the Thai military guys and 6 international divers went all the way in to the chamber where the kids and the coach were. That’s the 5 international divers we follow in the movie plus Craig Challen, a veterinarian who partners with Richard Harris (the anesthesiologist) and helped there on at least the last day of the rescue.