How should I continue? I have reached 2000 rating in rapid at lichess. I am a student, so I have to keep up with my schoolwork. I get around 1/2 to 1 hour on chess on each weekdays and 2hrs on weekends. My question is, if I want to get better, do I have enough time to get a higher rating or it's unlikely for me to improve? 

Thank you in advance.
With the time you say you have to spend on chess, of course it's possible to improve. You should remember that chess should never come first though, and it's just a game you enjoy. If you're not aiming to be a professional, don't spend hours on end every day studying it.

Here's a list of chess literature I think would benefit you, at your skill level:


Grandmaster Preparation series by Jacob Aagard. If you can work through all the books in it (I believe there are 5) you'll definitely improve.
My Great Predecessor series by Garry Kasparov. He annotates games of all the world champions (as well as many other strong players), and it's incredibly instructive. I also learned a huge amount of chess history from the series.


Other than that, it's good to continue playing online and doing tactics training. Even if you did only 1/2 hours per day of reading/playing/tactics, you'll start to see improvement. Also, since school should come first, I'd recommend not exceeding 1/2 hours per day, unless you're absolutely set on becoming a GM / professional (which I don't recommend).