What is in alavert? Could I be allergic to part of it?

Possibly. The active ingredient is loratidine, a newer antihistamine. Typically it is unusual to be allergic to an antihistamine, however there are more ingredients involved in manufacturing these products. Typically there are binders, fillers, coloring etc. All of these can rarely cause an allergic reaction.
Claritin (loratadine) Alavert is generic Claritin (loratadine). Unlikely you are allergic to the medication but it could be the coloring or additives to which you are reacting. Have you tried a different type of Claritin and been fine? If so, stay away from alavert.