Should I get a chess coach. Am I improving fast enough?

You probably don't need a chess coach unless you're planning on playing competitively when you get older. It sounds like you have improved fairly quickly. The best things you can do to improve is to read some books on chess. Try to read at least two books on chess every year, maybe more. A good book is My System by Aaron Nimzowich. It is not a book about openings but a book about all phases of the game. Another good one is called Maxims of Chess, but you might already know a lot of that stuff. You should check out your school library or public library first. Also learning from master's videos on YouTube can be very helpful. You don't need a YouTube account to watch them. The search bar is in the middle at the top. It'll drop down a number of hits and you might need to turn the volume on your computer up. I just play chess for fun, myself, and have no intention of becoming any type of chess champion. Leave a comment if you need more information.

Before you pay for a coach, join your local club. You will get free informal tuition and the opportunity to analyse and discuss your games. Believe me, it's the single most effective way to improve your chess game.