Ruhani You have wrong information. Surgery is not free for hijda's. Some hijda groups arrange for (illegal?) surgery from quacks in return for services rendered to the group like begging/sex work. That's what I saw in delhi/western UP area. I suspect these are organized gangs which are not always above the law. I would advise against getting into that scene. Take that option OUT of your book. NOW!
The proper approach is to go to a counsellor who will guide you through the process. The counsellor will take your assessment and give you the diagnosis. At the end of the procedure, If you are confirmed with Gender Dysphoria, you will get a letter from your counsellor about your GD diagnosis. She will also advise you on the possible course of action suitable for you. This could take upto 2 years. No doctor will operate on you (legally) without a certificate.
Surgery is expensive - between 80k to 4Lakhs. There are some states which will give you "free" surgery if you have the certificate from a govt approved doctor. But wait time for surgery can go upto 18 months.
I have been told that counselling is also free in Karnataka, apart from the initial registration fee of 400 rs. But I have not used it so I wont know. I must have spent 70K on counselling alone spread across 2 years till I got my certificate.