Do you think it might risk the future support of your parents if you start DIY behind their back rather than try to do it the proper way first and in a transparent fashion?

I can't tell your situation, but if it's possible they would be accepting and supportive of starting HRT, it might be worth figuring that out first and then starting HRT through a doctor if it's possible. Then if they aren't supportive, you can always start DIY knowing you tried the other way first.

If you start with DIY, you risk alienating the parents if they find out you are using DIY, usually people (doctors, parents, etc.) will not understand or accept that the risks of DIY are worth it. Getting people off DIY onto regulated, safe sources of hormones is seen as a form of harm reduction by doctors, for example.

I can imagine being a parent and learning my child bought unregulated grey-market drugs from the internet and have been injecting themselves with it would absolutely scare the shit out of me, and I would probably try to put a stop to that behavior, and it would certainly make me less sympathetic and more afraid of the whole prospect of HRT.