i can imagine the situation when a doctor say they didnt know what it was :)
But anyways i have gathered from your question is that you are definitely suffering from Urticaria
it will need a formal discusion to reach to a final type of it but i think cold or cholinergic urticarias must be differentiated at this point.
You have to do some labs aswel like a FBC,LFTS and a Urine R/E.
But the good news is you can use certain anti histamines
in the meanwhile
like Tablet Fexofenadine
180mg daily in the day and
10 mg in the night for atleast 2-4 weeks before you come up with your results.
Dont get so hopeless just try to discuss it with a dermatologist
that could it be certain type of urticaria and then i am sure he ll manage from there,
all the best