You don't have to be prescribed estrogen to have bloodwork done! I definitely think you should seek it out if you go the DIY route.
OP's not asking for advice on what to do with her therapist, she's asking for advice regarding DIY HRT. IMO it's not really our place to question why she might make that choice for herself.
I'm actually friends with one of queens mentioned in the article! These people are honestly so brave, every drag queen I know has received so many death threats in the past two years.
Last year, a couple of local queens I know were hosting a music festival, and a man was overheard heading into the venue saying "if those fucking f*gs come out on stage I'm leaving to get my gun". Thankfully he was arrested, but talk about terrifying. And yet these queens keep on fighting publicly for what's right.