Hello,
It is normal for a mole to fall off and may recur and the recurring mole can be different from what you originally had. Melanomas are usually >6 mm in size, with irregular borders, asymmetrical and dark in color. If you notice changes in the mole's/mark’s color, height, size or shape, you should have a dermatologist evaluate it. You also should have it checked if it bleeds, oozes, itches, appear scaly, or become tender or painful. Otherwise it should be left as such.
It is very difficult to precisely confirm a diagnosis without examination and investigations and the answer is based on the medical information provided. For exact diagnosis, you are requested to consult your dermatologist. I sincerely hope that helps. Take care and please do keep me posted on how you are doing.
How about you talk about this with your mum. She will reassure you I'm sure.
If skin is damaged, even moles, it doesn't look the same afterwards. Give yours a few weeks to recover and then observe over time for any changes. It doesn't sound at all worrisome but I am worried that you are asking this question on-line rather than talking to your parents. 13 year olds do go to the doctor if needed.
Take care.