I am also allergic to metal glasses frame. When I go to see my doctor, he recommend me to get titanium or stainless steel frame. Now I wear titanium glasses and I have no problem with them. I suggest you get titanium glasses which can solve this problem.
As long as you don't touch the metal, there is no problem then. Plastic glasses frame is a good choice. They are lightweight and durable and won't cause allergy to your skin. You can also choose titanium frames, however, they are more expensive than the plastic frames.
If you are allergic to metal glasses frames, you can try other glasses frames, like plastic, titanium, or stainless steel frame. You can also exchange for contact lenses. However, you should go to see an doctor before you wear contacts. The doctor will tell you whether you are suitable for contacts or not.