Your problem with gum overgrowing is not an unusual one, and it is usually something that should not be any cause for worry.
There could be many reasons why gums overgrow, and I will attempt to list them here in broad categories:
1. Gums overgrowing due to local irritation and inflammation.
2. Gums overgrowing as a side effect of certain medication (for eg anti-convulsants).
3. Gums overgrowing due to some kind of systemic conditions (for eg pregnancy).
4. Gums overgrowing due to benign or cancerous growths.
From your description, it seems like the most likely cause for your gum overgrowing is due to local irritation caused by braces and/or the rubber bands.
It would be best that you confirm this with your dentist to disclude any of the other potential causes as listed above.
When local irritation factors are removed, and with good oral hygiene, the gum overgrowth usually subsides, failing which your dentist could perform very minor gum surgery called Gingivectomy, to remove the excess gum tissue.
I hope this information helps, and I wish you all the best in your orthodontic journey!
Kind Regards,
Dr Gerald Tan