I'm allergic to a long list of things and 10-years ago spent a lot of time with doctors. I learned a lot - mostly that you are going to be the best judge of what you may have a problem with.
Doctors can do skin and blood tests to check for allergies to natural stuff - weeds, tree pollen, grass, dust, etc. They don't have tests for what they distinguish as chemical sensitivities. I'm very sensitive to something in perfumes. The only thing the doctors could tell me to do was to determine through trial and error what chemicals I was sensitive to, and to avoid them.
I did undergo allergy shots for the things I was allergic to - weeds, pollen, etc. After my allergies were reduced, I found my chemical sensitivities reduced, too. My body was healthier, and thus not so sensitive to chemicals.
If you think the darkroom chemicals are to blame, use good laboratory practices. The suggestions for ventilation and filters are good, but you should avoid touching the chemicals, too. If the problem continues, begin eliminating chemicals one by one to see what is causing a reaction. There have been good suggestions here - I'd start with the fixer and stop bath. Then I'd try eliminating metol and continue testing from there.
If you are chemical sensitive, you have a long journey, but through hard work, you can get better. When I began, I was so sensitive to perfume, I could not walk down the laundry detergent aisle at the supermarket to purchase the unscented detergent. I had to find a clerk to get it for me. Yesterday, I walked down the detergent aisle with impunity as I purchased a box of Arm and Hammer Washing Soda - sodium carbonate for my Pyrocat HD. Ha.