You are absolutely correct that the best ways to protect against skin cancer are to avoid prolonged sun exposure and to wear sun screen when you are out in the sun to protect your skin, so make sure to keep that up!
Other than that, it is quite common to 'discover' new moles, especially in areas that are hard to see such as the back. The mole may in fact have been there for some time, but you could just be noticing it now. Nevertheless, all moles should be watched closely because of the small chance that they could turn into melanoma, a serious form of skin cancer.
The signs that should make you worry about a mole and cause you to see help from a doctor
are the following:
1. If the mole is asymmetric.
2. If the mole has an irregular or blurry border.
3. If the mole has more than one color within it.
4. If the mole is larger than about 6 mm or 1/4 inch
5. If the surface of the mole is elevated or with significant texture.
If the mole meets any of these criteria, this raises the chance of it being concerning, and it may require a biopsy
by your dermatologist