There is a medium sized bump on my arm that I'm pretty sure is not a bruise (it's reddish) - it hurts when I touch it though - what else could it be?

Painful bump. May be an infection. Better call your doctor for an examination.
Hard to say? With just your description, I doubt many of us could give you a very good answer. A photo might help! More description may help. You health history, recent activities and other issues would come into play to help tell more what you have. I would say you need to see your pcp and get a diagnosis and treatment plan. Good luck!