Yes, you can say 빨리 좋아지세요 too.
Here are some related expressions:
- 빨리 나으세요 - 낫다: be cured, recover.
- 빨리 나아지세요 - 나아지다: get better, improve.
- 빨리 좋아지세요 - 좋아지다: get better, improve.
- 빨리 나으셔야죠 [나아지셔야죠 / 좋아지셔야죠] - (It's imperative) You should get better soon.
* ~셔야죠, ~셔야지요: means ~셔야 되지요. A more indirect way of saying it (sounds more natural to me).