Regarding BEd course for teaching..

The essential qualification for the persuasion of B.Ed course is a graduation - degree irrespective of the streams such as Science, Humanities, Commerce or even in the Engineering stream from a recognised university and for the Engineering degree, it must have the approval of AICTE.
Hence considering the eligibility - angle, you are eligible for the persuasion of the said degree but ensure that you have at least secured 50 percent marks if from the general catogary, for OBC there is a further relaxation of 5 percent and for SC/ ST a reduction of 10 percent will be offered.
Once you pass the B.Ed course, you will be eligible to apply in the Government Higher Secodary School as a teacher in the science stream provided you clear the written and oral interview conducted by the school - committee.
M.Sc course can be taken up from the distance education rout and one of the leading institutions in this direction is IGNOU offering you a recognised degree and has its acceptance world over. The other institutions in the similar lines are Manipal Distance Education Education, Andhra University, Kota Unversity etc. You can choose any one of those universities.

You are B.Tech. You want to be in teaching line. B. Ed is a 2 years course. M.Tech is also a 2 years course. After B.Ed you are eligible to become a teacher in any government or private school to teach Mathematics and sciences. But You have to get qualified in the entrance test. Then only you will get a teaching post in a government school. After M.Tech you can attend the NET examination and a pass in that examination will make you eligible for a lecturer post. In my opinion, the time and efforts for both the courses you have to put in are the same. If I were you, I will opt for M Tech.
Even with B.Tech, some private colleges are offering lecturer post of course for a less salary. While working as a lecturer you can do your M.Tech. Then you can become a qualified lecturer by appearing in the NET examination. While working as a lecturer you can do your Ph D also.

From your query it appears that you have a liking for teaching jobs. If it is so then going for B.Ed. will be a good option.

For teaching jobs the B.Ed. will be required and being a graduate you can go for B.Ed. from any place of your interest and can apply for the same. Once you get admission in B.Ed. after completing it you can apply for the post of teachers in schools and if selected you can join there.

Alternatively you can think of going for post graduation like M.Tech. or even M.Sc. and after that can try to qualify the National Eligibility Test which makes one eligible to poly for lectureship in the colleges and universities.

Another option is go for research work leading to a degree of PhD in which case you can directly apply for lectureship without going for NET.

So various options are open for you but you have to take a long time perspective of things in making your career and it will be prudent and wise to adhere to your area of liking and interest as in that only one can work hard and achieve significantly to overcome the cut throat competition in the job market today.

There are many articles related to these maters in this site (ISC) and I will suggest you to go through them to get a detailed information about each and every career line possible for the engineering graduate. You can even ask in the comments box below the article about something which you want to learn in more details as the authors do a lot of work before writing those articles.