I got liquid nitrogen treatment for sun spots on my arms about 2 weeks ago my arms have just healed but healed with these pink spots will that go away?

Yes: Generally the pink left after initial healing from cryosurgical treatment for sun damage spots will slowly fade over days to a few months, but often on the arms may leave permanent white spots, but hopefully they will heal with a normal skin appearance. Wearing sunscreens over the treated areas may help the cosmetic healing look better when it is done healing.