Anaphylaxis is a severe allergic reaction, and Urticaria Pigmentosa is a condition where your body generates a large quantity of mast cells -- cells that go into battle to fight allergens.
Consult with an allergist. You may be able to control histamine release and allergy/anaphylaxis with a prophylactic antihistamine medication allowing you to use Tylenol when needed.
I agree with Leesa_Antarctica that you must carry some form of identification that clearly shows that you have an allergy to certain things.
You should also talk with your doctor about your concerns and carry an epi pen with you as a precaution should you encounter such serious allergies.
Always make sure that your tell whoever is treating you, for whatever reason, the allergies you know that you have to those drugs.
You need to discuss these issues with your doctor.
Well, here is something REALLY important: make SURE you carry around an Allergy Alert chain/necklace/bracelet or card! If you are in an accident and are unconscious, this may save your life!
Also, important to note -- it is a classic "Drug-Seeker" technique (which annoys the heck out of doctors, because they "see right through it") to tell the doc "Oh, yes, I'm allergic to aspirin and tylenol and this and that," so that they can get PURE oxycodone, morphine, etc (for various reasons, one of which is that usually the pure narcotics are stronger meds than the ones mixed with tylenol). So, it is even more important, in your case, to carry around some sort of Official Documentation substantiating your allergies. That way, before the doc has a chance to say "Yaaaa Riiiiight...." you can be whipping out your Officially Documented Medical Record.
Anyway, as far as surgeries, dental work, etc., I would be more worried about what OTHER meds you may suddenly become allergic to (for example, the novocaine drugs used when pulling teeth, etc.), because as far as aspirin and tylenol, there's a zillion other things doctors can give for pain that don't include those.
And, most importantly -- TELL each and every doctor about your condition before they provide a treatment plan. Allergies, as you know, is/are serious stuff!
Only a specialist in your disorder would be the one to consult. I know once my dentist suggested beta blockers instead of pain killers.