Masters

You have been misinformed. With 5 years experience in after BTech you stand better chances in comparison to a fresh BTech to get admission in MS.

If you cannot pursue a full time MBA, you should do a part time MBA from a reputed institute. Part time MBAs are good if it is from institutes like JBIMS, KJ Somaiya, NMIMS as these institute has more focus on case studies, presentation, class participation and demography. You may also look for cert

It is very important to have your highest degree from a good place, as that counts everywhere.
You can do your graduation in India and can pursue Master’s abroad. This will help in shaping g your career as per your interest.