Phlebitis bruise on my arm for over 8 months. Should I be worried?

Maybe. Anything that persists for that long, when it looks like it should have gone away, is cause for at least some worry. If you had a phlebitis (vein inflammation) diagnosed 8 months ago and it's still there, the diagnosis may be wrong. Go back to your doctor, or seek a second opinion.
Yes. If not treated effectively from day one these problems sill continue and take even longer to resolve...A re-evaluation by your physician is recommended as this has carried on for far too long.