How long can I wait with skin ulcers to see if it goes away without seeing a doctor?

Not long. I see this question was posted over a week ago. If you still have ulcers, go see a doctor.
Never hurts to check. Most simple skin ulcerations can be treated initially with simple first aid such as cleaning and triple antibiotic ointment, usually applied once or twice a day. Persistent bleeding, increasing redness around the ulcer, increasing pain and simply non-healing after let's say 3 days of the above treatment are excellent reasons to have your pcp check it out.

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