Can I change my engineering branch after 1st semester?

Branch can't be change in mid semester, it can only be changed after completing 1 year and branch change is totally on the discretion of the college or university plus you need to have good grades in first year . Contact your college or university for further details

Yes, Most of the college provides branch changing options after the completion of the 1st-year. If you score an aggregate of 8.5 or 9 as it differ for NITs and IITs.