SJ,
I would keep away from the stomach for a while if it is causing you discomfort. You may also want to try the buttocks, I find it is the least painful of areas to inject, but just bear in mind that the absorption from this area is the slowest of all the areas to administer insulin, so you may find a small delay before your insulin kicks in.
Failing that, you could ask for a meeting with your dsn and demonstrate your injection technique, she/he may offer some advice to avoid the pain/bleeding by observing your procedure.
Nigel