My 3 year old has allergies which I treat with Claritin, but now he has hives on his legs! Can I give him Benadryl (diphenhydramine) and Claritin at the same time?

Yes. Those two medications work very differently on allergies, and it is ok short term for a few days to combine the two if you need to. Also make sure he gets plenty to drink as both of these tend to dry up mucous membranes and he may feel very thirsty.
Claritin (loratadine) It is not necessary to use both medications . The Claritin (loratadine) should help for the hivesgive him a dose in the morning as well as a dose at night if necessary.