I'm sorry you've been having so much trouble. I don't know what size needles (gauge or length) you are using or about your anatomy, so I am speaking generally.
I do not mean to make light of your frustration, because it is genuine. Sounds like you've had sucky experiences. However, I am EXTREMELY skeptical that you hit a vein 7 times in a row and then hit a vein 3 more times unless you are doing something very very wrong OR you are misunderstanding what it means to hit a vein. It's almost statistically impossible to do this "by accident" if you're injecting in the right space of your body and with the right size/gauge needle.
By hitting a vein - do you mean that you are aspirating (pulling back on the plunger) and seeing blood drawn into the needle? That is what it means to hit a vein. If you have done so - 10 times you have stuck a needle into your body, pulled back on the plunger, and seen new blood enter the syringe - then, OUCH. That sucks. AND - that's a lot of wasted needles/syringes AND T - because once you aspirate blood into your needle, you should be starting all over with a new one!
But please be aware, that you have not necessarily hit a vein just because: you feel pain, you see blood when you remove the needle OR your leg bruises afterwards.
If you are aspirating and having blood enter into your needle 10 times out of 10 tries, then you are doing something very very wrong, and you should probably visit a doctor to see about how this can be avoided - whether it means injecting in a different part of your body, using different size/gauge needles or something. This is something that should not happen. If it has happened, please see a doctor to talk about what you can do differently.
If you are not aspirating & seeing blood enter the needle, and you are just experiencing pain or seeing some blood when you withdraw the needle, then you are NOT hitting a vein directly, as you think you are. You may be sideways nicking one (is your needle entering your body at a 90 degree angle?). More likely, you are experiencing pain & trauma to the area from being tense when you inject (which is understandable - I'd be tense if I thought I was hitting veins!) and from re-using the same needle after withdrawing it from your body. Each skin piercing dulls your needle, so the repetition makes it more likely that you are causing trauma to yourself that will bleed.
If this is the case, then I think you need some way of relaxing yourself adn starting with a clean slate. If you're switching sides (which you should be), do the side that you're better at. When injecting across the body, many people don't enter the injection site at the appropriate angle, for example. Beyond that, I don't know what method of preparing to inject calms you, but you really just need one positive experience to build on & to keep building each time from there. Whatever relaxes you and keeps that muscle relaxed, you'll have to find that. It may hurt a little or bleed a little, but remind yourself -that's ok. THat happens. That is NOT what it means to hit a vein. You'll be fine. Each time, it'll get easier. If you can't do this alone, you may need to have someone do your next injection for you or watch you do it, to give you confidence that you're doing it "right."