I have a small bump (maybe cyst) on my pubic area that will puss sometimes. Should I be worried? What can it be?

Maybe? Infection? In the pubic area, this is most likely an infected hair follicle or small skin abscess. It could be due to MRSA a very common and painful staph infection seen commonly today. You may have a sebaceous cyst as well. If it were lower down on the lips of the vaginal area, one would be concerned with a bartholin's cyst. Use lots of soap and water, antibiotic ointment and observe. If worse get seen.