What will happen if I accidently inject myself with a couple small pieces from the stopper
it'll be gross. I would strongly recommend against it.
They would stay in you essentially forever, unless cut out. Whether there would be adverse effect from it or not, I cannot say. It might even vary depending on the material of the stopper.
If it's already happened, well, monitor the area from now on. If there will be trouble from it, there might be a long onset before any sign appears.
If it hasn't happened and you're just wondering if you need to throw out a vial that has such particles in it, either filter out with a submicron syringe filter, or throw out. If it's merely a syringe with it, throwing out would be my advice.
I don't know if this is good to do or not, but I have 5 cc syringes, and I usually pull a few injections worth out of the vial at a time, and just change needles each time. This way I don't have to poke the rubber stopper so many times. The longest a syringe will last is about 3 weeks tops. This is especially good while cruising, with a bottle of t 400 when you are running 250 a week or so, that would be way too many jabs through the rubber for a small amount of gear.
Usually you can see where you pierced the stopper the first time. I just slide it in