Could I be allergic to my cat ?

So I just adopted a kitten a few days ago...and now my throat is really itchy, like there is a lot of mucus but I can't spit it out... it feels like there was hair in there or something... I cough a lot and clear my throat with no success... i'M hoping it'd be just a cold, as it is winter...I've owned cats before and had no problems, my aunt has cats and I was over there last week with no problems.. But I did discover one hive today on my arm, nowhere near any scratch tho...and only one so far... all the cats mentionned are no specific breeds... some long hair some short... when my kitten scratches me it doesnt do any thing weird, itch or swelling or anything... same when she leaves me... i don't have any other symptom of allergies or of cold, no stuffy nose no runny eyes no rash... I'm wondering if it could be that I would've become allergic to my kitty ???