Hello,
what your suffering with is a condition called contact dermatitis, as soon as the allergin is in contact with your skin you breakout in a rash.
Although the mask may not be made out of latex it will probably be manufactured using a technique known as vulcanisation (more commonly known as rubber acceleration) which uses all sorts of harmful chemicals, and its these chemicals that 9/10 are causing your problems.
Your position is somewhat unfortunate becuase your going to need to be in contact with this stuff at some point.
You need to go to your doctor or dermatologist and they will probably give you a topical steroid cream or perhaps a barrier cream to apply before being in contact with the rubber.
You could try an antihistimine to relieve any discomfort such as itching, xyzal/levocertizine would be a good one to try