Microdermabrasion for Sun Damage on Arm?

The best thing you can do now is to consistently apply SPF 30 or greater. I'm sure the sun is strong in Louisianna, and the effectiveness of any intervention will be related to how well you can protect the area from UV rays.
After the summer, get evaluated for IPL treatments that are highly effective at lightening the brown pigmentation.
Best regards.

Thank you for your question.
Microdermabrasion to your arm would likely not give the results your looking for. In my opinion, try practicing strict sunavoidance, use a strong sunscreen, and ask your dermatologist for a hydroquinone prescription. Your dermatologist will also be able to prescribe you a higher percentage bleaching cream that the customary 4% hydroquinone, and that will likely (over time) give you the result you need.
Good luck!