WE BEAT THE NEWS MEGA
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It takes a lot of very careful and skilled work to inject in a vein. I know because I do it at work. You don't accidently inject in a vein, don't worry.
How much bleeding are we talking here, cause what I think is concerning bleeding and what you think is concerning bleeding is probably not close. A little daub of blood at the end is fine and normal. A bit of bleeding is fine and normal - especially if you're taking any blood thinners or aspirin. If it's 3 hours later and you've had to change bandages a few times and it's still actively bleeding - that's making me think "this is concerning bleeding"
It was not a concerning amount of bleeding, and it has stopped. It was just more than I am used to, but based on your description it wasn't anything extremely out of the ordinary. Thank you for this, I really don't trust myself (especially with this kind of stuff) but it helps know it's not something that can be done by accident.