Hello,
If the rash that you describe is red, itchy, has raised skin that you can feel, goes away after a few hours only for new ones to appear in their place, does not leave a mark or bruise, then this is acute
urticaria. That you have had it for >6 weeks, makes it chronic urticaria.
80% of people with urticaria do not have allergy, although a pre-existing allergy to (say) house dust mite, pollens or shrimp does not make it more likely for this type of urticaria to appear.
Infections, underlying thyroid problems,
diabetes, inflammation inside the body (can be several conditions, say
endometriosis) and stress makes these lesions appear and can last quite long.
The treatment (that you don't like) is the right one, long-acting non-sedating antihistamines like allegra 180mg once in the morning, and
cetirizine 10mg at lunch time or evening for 6 weeks (max 3 months). Unless you continue on high dose antihistamines, this will recur.
If you think you may have a thyroid problem, get TSH fT4 and TPO
antibodies tested.
If there is a chance of an infection, please get this checked and treated as well.
I hope this helps.
Best Wishes.