No need of vaccination again and basically both covisheild and covaccine are equally working and having equal efficacy. Go through the covid-19 antibody test which indicates the development of antibodies against the corana infection.

Usually not needed, contact you college administrators about the issue

Ya I get your point . It’s not the immunity but you need Covishield to be recognized as a vaccinated individual when you trace l in immigration. If you have crossed 3 months since your second dose of Covaxin you can technically take Covishield dose 1 . But I’m not sure if the Cowin app and other agencies allow if. Medically it is safe to do so after 3 months