Hello I have gone through your question and understand your concern. Consult a doctor, get per rectal examination and colonoscopy done. The discharge appears to be pus and most likely it can be due to abscess from infected tear in rectal area. Sometimes hard stools, constipation, straining due passing stool and hard food can cause rectal tears which may get infected over time and turn into an abscess. Antibiotics, drainage of abscess along with aseptic dressings can treat the condition. Till then follow the procedure of Sitz bath, that is soaking your bottom in warm water (add betadine or Epsom salt) for few minutes. Use lignocaine 2% jelly( available over the counter) instead of petroleum jelly to minimize the burning sensation. Hope your concern is answered. Thank you.