Hello,
If the cyst has burst, you should not squeeze it out yourself but should let your doctor do it under aseptic conditions so that infection does not occur. You may also need to apply topical antiseptics and topical antibiotics. If symptoms are severe then you may need oral antibiotics as well.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your doctor. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
I have had plenty of cysts in my life. If you squeeze out all the pus and then disinfect the wound, you should be fine since the cyst is right on the surface. If you have some antibiotic ointment you can use that.