Since your elbow is a high-mobility joint, healing can take longer. Oral antibiotics (like cefixime) are usually unnecessary for superficial wounds unless a spreading infection is present. For better healing, focus on local wound care: gently clean the area with mild soap and water, apply a thin layer of petroleum jelly or a generic triple-antibiotic ointment, and keep it covered with a sterile bandage. For pain, over-the-counter paracetamol or ibuprofen can help. Please consult a doctor to examine the elbow. They can ensure there is no deeper joint damage, trapped debris, or resistant infection causing the delayed healing.