Not sure if this information will help, but I did some searching and it appears that sunscreen allergies are common. There seems to be 2 classifications - a contact (allergy manifests by applying the sunscreen to your skin), and a photoallergy (allergy manifests when the sunscreen reacts under exposure to the sun/UV radiation).
In your case, does your reaction occur after contact only, or after you step into the sun? If you haven't noticed, may want to see test which is your reaction trigger. From there, you may be able to try to narrow down what in the sunscreen you react with.
I did find there are hypo-allergenic sunscreens available - if you haven't looked for them, you may want to search the web to find some brands to see if maybe those will work for you. Those seem to be made using natural ingredients vs chemicals.
You'll probably read the most common manifestation of these sunscreen allergies is some sort of rash or other skin reaction, however sounds like your allergy triggers a different manifestation - which may be rare, but not unheard of.
I have an allergy to alcohol - my mom and grandmother broke out in a rash when they drank red wine; for me, alcohol triggers an asthma reaction (doesn't matter what kind of alcohol - they all trigger it). I have a wider allergy to alcohol, but a different allergy reaction. Probably the same with you.
If you are unable to identify what is triggering your reaction, or find an alternative product - only safe options for you is to avoid sun exposure, and use hats and light weight long sleeve shirts/pants when outdoors for any length of item. Sit under umbrellas or anything to shade you from UV rays.
Good luck to you!