What should I do about my study of gym sports, which requires immodest clothing, with the presence of young men and listening to songs, and in the event of not practicing, I am asked to provide a medical certificate, which may force me to cheat and lie?

It is not permissible to study in mixed schools except under specific controls and conditions, just as it is forbidden to listen to singing and music. It is also not permissible for a woman to practice sports with non-mahram men. If the Sharia-compliant controls for studying are met, then it is permissible for you to study without engaging in sports. If you need to study and find an exemption from sports, even through lying and deception, there is no blame upon you; rather, you will be rewarded for it, because preventing the forbidden is obligatory.