Based on the description provided, the painful red bump on the outside of your right buttock may be a furuncle or an abscess. Given the presence of general symptoms such as fatigue and loss of appetite, as well as the lack of improvement in the lesion, it would be advisable to consult a doctor for a proper evaluation. In the meantime, monitor your temperature, avoid touching or attempting to puncture the bump yourself, and apply warm compresses. Maintain good hygiene by cleaning the affected area with water after bowel movements and urination.