About post-blood donation symptoms?

I donated blood recently and I fainted straight after the procedure. I was donating under 10mins, at approx 500ml. (50-60ml/min). At the injection site there is bruising and it is very swollen. (purple with a few red lines in the bruise). I also had a mygrain after the incident despite plenty of fluids being taken. I am uncertain whether or not I have injured myself anywhere else but my chin, whilst being unconscious.
Any explanations for the physiological reasons for these events?

You can find a lot of information about the fainting with a simple internet search. Fainting after donating is not uncommon. Donating blood reduces your blood volume, which forces your body to compensate to maintain blood pressure. Some people's bodies compensate better than others. There can also be other factors at play (e.g. look up "vasovagal").

Simply taking fluids when you donate is not enough if you were poorly hydrated beforehand. Hydration can be built up (or depleted) over days, and can't be instantly corrected by a couple of glasses of water. The concentration of your urine is a simple guide.

As for the bruise, a bruise is, by definition, broken blood vessels - they have to break a vein in order to draw your blood, so a bruise is inevitable. I've given blood many times and sometimes the bruise is barely noticeable, other times it hurts for days. Might depend on the skill of the nurse, I don't know. Also helps if you can rest the arm (or at least not work the elbow too much) for the rest of the day.