I am currently using Mederma (I think that’s how it’s spelled…) on my thyroid surgery scar. I have used it in the past as well for an injury on my face. Though that was much more shallow than my new scar. People have also recommended that I rub vitamin E on it, though I haven’t tried that yet.
It is also a good thing that you are keeping them out of the sun. I have to wear a (silk) scarf for the next year or two, even in 103 degree heat! I know how much it sucks, but it is going to be worth it! If you do go sleeveless, make sure you bomb your arms with sunscreen. My scar is very deep so I’m taking extra precautions, but if yours aren’t too deep then a good sunscreen should help loads.