You should seek a dental evaluation as soon as possible. The most likely cause of the red bump may be trauma from the broken tooth. There may be a sharp spot on the tooth that's rubbing your tongue a little raw and making it red. You should really take care of that broken tooth before it gets worse and can result in an abscess where the infection spreads.
As for the pain, its possible you may have something going on with the other tooth as well or what we term, referred pain. Referred pain is when there's pain in one area but it feels like its somewhere else due to the complexities of the nervous system of the head.
Thank you for the advice. Right now, I do not have any dental insurance and I applied to see if I'll be able to see a mobile dental service for low-income or people without dental insurance. So, if I get accepted, I'll be able to get my teeth checked until then I'm out of luck.
You may want to contact your local dental society or surrounding dental societies to inquire if there are any local organizations or dentists who may provide free/discounted dental care for low income individuals. I'm assuming that you live in the United States.