You would be a great candidate for laser hair removal to reduce the amount of ingrown hairs and number/size of the hair follicles in the area. You may require 6-8 treatments approximately 4-6 weeks apart. Best of luck!
It should not be a problem to have laser hair removal while on Doxycycline, also you can have your eyebrows waxed. Check with your laser specialist first or call your dermatologist who prescribed the medications to make sure they are comfortable with that. Good luck!
I am assuming that you are referring to bikini laser hair removal. Yes you can. The laser would not penetrate enough to disturb or interact with your iud