I got a very bad bruise that is also burning on the same arm I had an IV in today, should I be concerned?

Probably not. This is probably a short term problem that will clear up. Put ice packs on it several times a day. Arnica can also be helpful. If it's not clearing up after a couple of days, or if symptoms increase, have them check you for complications.
Yes. Bruising in that area is common. It will go away in a few days. Check for any red streaks travelling from the injection site, and for any fevers. Those may be signs of an infection. In that case, contact the provider who administered the iv.