Can they check out my pet she is itching and losing hair

It is a well check clinic but if it is caused by fleas they can get medicine started to fix that.

They have no diagnostics and only preventative medicines (flea meds, vaccines, ect.) So you won't get a lot out of the visit since they can only help if it's flea related

Most likely a flea allergy. Epet can get you a good flea preventive