You are really courageous to take steps towards your transition while living there.
I grew up in a similar environment in a country (which I will not name for the sake of privacy and safety) where trans individuals could be brutalized with no legal consequences. During childhood, around age 5, I observed absolute ostracism and horrible police brutality towards trans people. The laws did not recognize them as human beings and they had no legal recourse, no access to residential areas, no access to education and no access to employment. They were seen as criminals by their very existence. Some people there were proud that they had physically hurt trans individuals, like a hunter would be after a big kill.
I had realized by age 3 or 4 that there was something wrong gender-wise, with the world or with me, but I was too young to articulate my feelings. When I became old enough to articulate my feelings, I had already observed atrocities towards trans people. After my observations in that country, I learned to hold all my feelings inside and never talk about it with anyone. I knew that getting out of that country was my only way out and great education was my vehicle out. I focused on academics which also served as a distraction from the gender incongruence I felt. It took me 6 years of living in the US in a very liberal area to overcome my fears and finally begin to explore the possibility of transition.
Although I live as female now, I have not updated any of my old documents from that country. I am not coming out to anyone from that country (except my sibling who is totally supportive and my parents whom I have not told the entire story yet). I have not interacted with my relatives from that country for over 15 years, not kept in touch with any friends or classmates from that country for over a decade, and not socialized with anyone from that country in over 2 years. I know I may be going too far, but my parents still live in that country and I care for their safety.
Based on your post, it sounds like India is no better. I have a few questions, not trying to pry or suggest better ways; merely trying to understand the situation in India.
It sounds like you do not identify as hijra. Per my understanding, hijras are almost like a religious cult of "neither men nor women". They choose or end up with this designation of hijra because their are intersex, or because their families were illiterate enough to not know what to do with their baby who had some physical deformity, or due to some cultural/religious/social compulsions (I do not totally understand these compulsions), or because they were kidnapped and genitally mutilated. A lot of people with gender dysphoria end up among hijras in India, not due to choice, but because they have nowhere else to go once their family and their society disowns them. So not all hijras are actually technically hijras, as many are individuals with gender dysphoria. Have I got this right?
Why do people in India not distinguish between the hijras and people with gender dysphoria? Is it primarily due to the lack of distinction between reproductive/genetic sex and psychological gender, or lack of knowledge/information, or is there some other religious or social or cultural reason?
I have heard that people from India classify all LGBT people as hijras in their general conversation. Is this true?
Would you be able to live socially as your gender assigned at birth while you transition, not show any many outward signs (eg. behavior, mannerisms, etc) that you may be trans, and when you are ready to transition socially just move to another part of that country and live in your right gender without anyone figuring it out? I understand that this may be hard, both mentally draining and difficult to execute, but is this possible at all?
I have heard that India does not permit changing gender on the birth certificate from M to F and from F to M, but it has recently allowed people to change their gender on the passport from M to F or E or from F to M or E (E = eunuch, which I find insulting if used to describe me, and even invalid because I saved my sperm before my transition and I am only as much of a eunuch as everyone with infertility issues and everyone over a certain age and everyone susceptible of getting into an accident tomorrow!!!). Would you be able to get a passport in your right gender and use the passport for all identification within India and thereby not have an issue within India?