Hey, I know anxiety isn't always rational (usually not, in fact), so what I'm about to say might not actually help you at all. Still though, I'm going to say it.
HRT injections are pretty idiot-proof. If they weren't, it wouldn't be so common for people to self-administer them. If injections were easily messed up and dangerous, quite a few of us would have weekly appointments at clinics to have professionals do them, but we don't. My sister didn't even get any training on how to do her injections, she was literally handed a pamphlet with instructions and diagrams and told "go for it".
Injections are absolutely scary, I don't like doing them, but I always remind myself that there's nothing that can go seriously wrong. Some weeks hurt (or bleed) more than others, but that's the extent of it. There's nothing I can do to actually cause injury or to cause the hormones to not work or something.