Sometimes little cysts appear. They generally disappear on their own. It could be a tiny ulcer. If your teeth are loose then it sounds like you need to have your gums looked at and have a dental hygeine specialist suggest an appropriate dental hygeine routine.
I am a dental hygienist. the red bump could be anything, an typical ulcer does not usually present as a bump but as concave. I would get it looked at at your next hygiene appointment unless you notice it growing in size or changing in appearance other than disappear.
Your gingiva "gums" should not be loose and is usually associated with gum disease. Healthy gingiva appears peachy in color, not red, no bleeding, tight, stippling like the surface of a lemon, no puffiness. You should set up a hygiene appointment and start brushing 2-3x a day minimum and floss every night before bed. Using a mouth rinse such as listerine or crest pro health (non alcoholic) when you brush would help. Change out your tooth brush. You do not have to wait for your hygiene appointment to start a healthy routine.