No, You are not screwed at all .You secured a decent rank in JEE Advanced with this rank you will get branches like metallurgy, biotech,textile,chemical in old IITs and branches like civil,mechanical in new IITs. Now,it’s up to you what will you prefer branch or college . You can enter in old IITs with an average branch and work hard in the first year then you can upgrade your branch. If you get a branch of your dream even if in the new IITs then go pursue your passion .

You also secured good marks in BITSAT with this marks you can get branches like electrical,mechanical in BITS GOA and hyderabad and branches like civil, chemical in BITS PILANI. You can also upgtrade your branch in BITS but for this you have to score above 9.5 cgpa.

Now, it’s upto you what you choose .

GOOD LUCK for your future .