When I was a child I accidentally drank overdosed on penicillan and had severe diarhhea. Then I developed hives. Is this an allergic reaction?

Possible not likely. Medication allergy is usually an immediate IgE mediated immune response. In this case the hives would have been expected to come out first. Your hives were probably a stress related reaction to the diarrhea and the overdose amount of penicillin. An allergy specialist can do tests to check specifically for penicillin allergy and if negative, you will have access to an important, cheap class of med.