In all honesty, I don't think there is anything wrong with using drive to escape pressure. In fact if you find a hole in your opponents pressure then you should use drive to get out of it. The problem with over using drive is that your opponent may start to punish for it. Which is why you shouldn't use drive on wake up so often.
As for escaping pressure, the best advice I can give you is to learn the each characters blockstrings. A lot of them have a lot of holes that you can poke/backdash/drive through, and if worst comes to worst you can use your counter assault on a move that has a lot of recovery and punish them with it.
(Also I wrote this kind fast of so if It doesn't make any sense I'll try to explain it better. Don't give up, I still think your a good player.)