Should I take a drop this year or should I join some college and prepare side by side for IIT-JEE 2018?

Sir you are yourself writing that you deserv better than this then you must go for a drop. Also since you could not perform in JEE inspite of good marks in FITJE which is a very good institute, means you need to focus on last year questions a very good revision.

You dont need to ask anyone and focus on your trust and confidence. If you think you can perform better than you must go for next year.

One thing which I would like to suggest you is that if you want to qualify JEE than just focus on that. Riding on two boats is quiet dangerous and useless.

Rest up to you.
All the best