Last year I received an extremely bad sunburn on my upper arm. It was very bad, it blistered and scabbed up and took about two to three weeks to heal completely. It was about a one and a half inch sore. I don't know why it happened exactly because I was liberally applying sunscreen, but apparently missed the upper left arm. My question is that I constantly observe the area to see if there are any suspicious moles growing there, should I go to a doctor now to have a check up in that area now before anything really strange appears. The area has healed completely, however, I am worried when I see some freckles there that I had never had before. Can this eventually turn into skin cancer? How long can it take? I am somewhat nervous about this since the burn was so bad. Thanks for any insight

Just because you had a bad burn does not mean that for sure you will develop skin cancer in that area. Repetitive sun burns can lead eventually years later to skin cancer, but people also develop skin cancer in places where the sun never reached. So I would not worry myself over this.
Just notice anywhere on your body if something new develops and quickly grows larger. Like bigger than an eraser head on a pencil.

It would be prudent to go see a dermatologist for an entire body mole check. This way he/she could make sure that your skin is fine.