Shaving help for sensitive skin?

Whenever I shave my legs, no matter how gently I shave or how much I lather up, my legs always end up burning and covered with tiny red dots (this is usually just on my inner calves). I need to shave every day since my hair grows so fast, so it's really difficult for me to deal with the pain that often, or the unattractive redness that covers my legs. I've tried the new Veet wax strips, but they too leave my legs in the same condition. Is there anything I can do to fix this? I'm really tired of this D: