Red bumps on hand and face spreading to back and arms. Er said allergic reaction. Cream not helping at all. Itch bad only hand. Help. Contagious?

Derm problems. Dermatological problems are very difficult to diagnosis without actually seeing the problem. If the er is correct in the diagnosis, allergic conditions are not contagious. Most creams used to treat allergic reactions are steroid creams. If one cream does not work, stronger creams are usually available. See your doctor to confirm the diagnosis and to discuss the possibility of a stronger cream.
No idea. First of all er docs, god bless 'em, are clueless about skin. Not their fault, they're trained to save lives, not diagnose rashes. "allergic reaction" is a non-diagnosis; and the list of possible causes of "itchy red bumps" is a mile long. You need to see a dermatologist and get a precise diagnosis.