Yeah. The bacteria that Tetracycline fights will grow resistant of it if you keep using it. However I have no idea why they would give you that for a venom injection, unless they're going to treat the side effects of the venom. What kind is it? It makes more sense to create an antivenom for long term needs. Which I can't do. Sorry but you'll need a different person for that, like I said my specialty is plant poison.
You can try a thick glove? If the cat isn't biting you to inject venom you might be able to get away with it.