All local anesthetic used in dentistry today are amides rather than esters. With the old ester-type locals (no longer used), cross-allergenicity did occur, so if you were allergic to one ester-type local anaesthetic, all the others were contraindicated.
The good thing about the amides used nowadays is that cross-allergenicity does not occur. In other words, allergy to one amide local doesn't mean that you're allergic to other amide locals. There are five amides in use: lidocaine (which it sounds like you're allergic to), mepivacaine (carbocaine is a mepivacaine), prilocaine, articaine, and bupivacaine.
An allergist can test which ones are safe for you.
Most people are allergic to the preservative rather than the anesthetic.
Lidocaine and Xylocaine are the same thing. You'll probably be fine with Carbocaine
I would think that you should consult an allergest to determine which of the caine drugs you can take.