Hi I had a similar experience with a mole on my leg. My doctor ended up taking more skin from the area just to be sure that there were no more atypical cells surrounding where the mole had been. They also wanted to make sure that the mole wouldn't grow back because it might have became a melanoma later on if it did. I don't think you are overreacting and I do think you may have a higher risk of melanoma than other people.
I also used to use tanning beds for many years, which I now regret. Melanoma doesn't have to run in your family for you to get it. Melanoma can be completely brought on by ourselves by too much sun and tanning beds. So if I were you I'd wear sunscreen every day, don't tan, and get skin checks at your dermatologist every 3-6 months depending on if you notice any changes in your skin. You can never be too careful because these things can sneak up on us. :)
Kinda overreacting in my opinion. Lots of people have risk factors for melanoma and you have a couple (tanning beds, atypical moles). Some people have way more, like a family history, a melanoma in the past.
It pays to keep and eye on your moles and see someone as soon as you notice any changes.
Enjoy your good health and excellent biopsy result.
Take care.