Is this a rash?

i've been having this for a month now. started from a right hand where i cut my finger a bit and it was on other side palm the next day went to clinic, doctor said it isnt a rash but an allergy. i had a unprotected sex too and these all happened after having anxiety of possible infection from hiv.

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looks like eczema

hi cathrine, thank you replying. what bothers me the most is it doesn’t itchy at all and it becomes pruney for few minuates after soaking in a water. and it was all over the palm but now its in mostly near the tip of fingers.and also is it possible to create a lymph nods because of eczema?