So, a few things: DIY is not as risky as it sounds, it's a grey market and last time I checked, you can often just buy the stuff you would have been prescribed, i.e. lab-made, pharmaceutical-grade, FDA-regulated estrogen - but a lot of people buy vials that are compounded not by professional labs, which does carry more risk obviously, but those vials are occasionally tested and there haven't been any major incidents or risks as far as I know - so the consensus seems to be that DIY is safe and effective, and you should absolutely consider it an option.
However, since you're in the U.S. there is absolutely no need to go DIY when you can get it through a Rx. There are no mandatory wait times for estrogen in the U.S., you don't usually have to even have a letter from a psychologist. I personally called my primary care physician and told them I have gender dysphoria, and they sent a referral to an endocrinologist I had found that treats trans patients. I did have a three month wait to see the endo, and that is a time I wish I could have gone back and been on DIY while waiting, but when I saw the endo, he prescribed me estrogen that day and I went to a pharmacy and had it filled same-day.
Some IRL friends just go to Planned Parenthood, who have doctors you can see and who operate on an informed consent model, which means you don't need a letter but you can just consent to taking HRT.
As far as diagnosis, those medical records should be private but I absolutely understand the concern. You will need a proper diagnosis for some procedures to be covered by insurance, so something to consider is the long term there - you may not be able to avoid a diagnosis forever depending on your medical needs, but with the Trump admin trying to force hospitals to turn over records I can understand the concern.
Regardless, this is where I would connect with your local trans community and ask which doctors they see. I used to live in the South where trans healthcare was banned for minors, but if you knew the right people, you could still find doctors who would treat patients. One of the ways this is achieved is by the doctors using a different diagnosis code, for example. I have also heard of doctors offering to delete or scrub references to the diagnosis from the medical chart.
So this is a discussion to have with your local trans community and with the doctors they recommend - you may be surprised at what they can do to help you and what your options are. And if that falls through, DIY is a safe, effective, and reasonable alternative (despite how sus it may seem).
And regardless, I think the politics again shouldn't drive you away from treatment, but towards it - concerns about diagnosis are wise and worthwhile, but if your fear of a diagnostic record existing means living as a visibly trans person for longer, the real risks of delayed treatment might be greater on the streets than the potential risks of a medical record existing and later implicating you. Realistically, once we are at the level that a gender dysphoria diagnosis in your private medical records are a direct risk to your safety more than not being cis-passing, you should realistically be fleeing the country.
It might also be tempting to think you can avoid persecution by just not transitioning, but the reality is that you can't choose to be trans, and whether you transition or not won't change the fact of your gender dysphoria - among your options, living without care is one of the worst ones, and the risks from transitioning are overall still lower.