Irritation after a procedure
I am not sure what the "black speck" that was in the wound. I would return to the physician who treated you and removed the mole to make sure it is healing properly and continue to use good wound care in the interim. Please let me know what happens at the dermatologist.
Irritated site after removal
You are fine. It would be best to clean your site with a qtip and not press too hard, but you haven't done anything bad to the site. Keep the area well gooped up with Aquaphor or Vaseline.
"This answer has been solicited without seeing this patient and cannot be held as true medical advice, but only opinion. Seek in-person treatment with a trained medical professional for appropriate care."