I failed popping my cystic pimple. now it's still got puss, and it's inflamed and purple. is there a way of treating this at home?

Cystic acne: Popping pimples/cysts not a good idea: can drive infection deeper. Warm-hot compresses can draw cyst to head so it opens on its own & drains. But best treatment is to see dermatologist for definitive care of acne: topical meds + oral antibiotics; possibly accutane-like product if condition is severe. Should also be checked for polycystic ovarian ds by doc.