To find an answer whether there is a way for me to excercise without getting heat rash?

There are: effective anti-perspirants....available by PRESCRIPTION. Ask your Primary Care Provider for a suggestion or referral to a Dermatologist!

Loose clothes: Tight clothes can make it worse. Also be sure to use unscented soaps, deodorants, lotions on body and clothes. Some fabrics breathe easier allowing lower temp build-up and can wick away moisture which helps, too.. Obviously, cooler surrounding temperatures help. If persists, get checked and find out if there's something else going, including metabolic problems which affect temperature regulation

Focus on: wearing clothing that is breathable and wicks away sweat. Often the best clothing is so called "technical" gear made out of synthetic fibers. Additionally try to find an area to work out that has great ventilation and air-conditioning. Avoid wearing clothing that is too tight fitting. Best of luck.