Well brother, I can understand your situation. I know you have worked hard for JEE advanced but I believe with 3.6 category rank you won't be getting any decent IIT which I can recommend you.

Though with OBC, there might be an increased chance of your's getting a seat but with such a rank it is very hard to get.

As, opting a very low rank IIT core branch will bring nothing good for you which lags even the permanent faculty and infrasture to nurture you.

So, I would suggest you to prefer state engineering colleges or decent NIT's.

Also, I would recommend you to do take part in JoSAA and go to through all the round even the spot round. May be, some good fortune can turn your destiny.