respected sir,

there are lot more opportunities in order to do b.tech after 12th. for getting an iit seat you have to write iit exam very well besides there is an another opportunity called AIEEE in which you will get seat in NITs

there are also state boards which will conduct regular entrance exam if you qualify that exam you are eligible for applying b.tech in all b.tech colleges of your state

there are also deemed universities which will conduct separately.

Yes you are eligible . As you don't have a gap after your intermediate.  I suggest you to write eamcet, jee mains, or mains if you wish to persue btech or else go for degree and try to attempt the competitive exam like bank tests,gate,ias,ips,ifs if you wish to do government jobs.

Hope this answer helps you. 

The eligibility and admission criteria vary entrance and college wise so kindly share which one you are aiming for?