It's very rare to actually be allergic to an odor, but many people are sensitive to strong smells, whether it's burning rubber or strong perfume, and the results are pretty much what you describe, so whether you're actually allergic or not may not matter.
If you're actually allergic to the smell (or possibly to tiny rubber particles that might be in the air), antihistamines might help with your symptoms. If you're sensitive to the smell because it irritates your throat and sinuses, the antihistamines won't help - your body is reacting the way it's supposed to when you're exposed to something that might irritate the lungs and sinuses, and your best bet would be to try to avoid the irritant.
