I have a little red cystic bump on the right side of my chin, every couple of months it flares up into a huge red bump then goes down to a little bump again. why wont it ever fully go away?

Skin cyst: Bumps that behave like this can be skin cysts that periodically get infected and then get better, but never go away. A cyst needs to be excised to completely eradicate it.

The cyst remains...: It will be easier to make recommendations after an md examines you, but most likely the lesion never goes away because the cyst itself below the skin remains. It is like a little bag of debris that gets infected. If/when the cyst is removed the lesion will not recur.