Sounds a lot like she has mites. Did you get her from a petstore? Almost all pet store guinea pigs end up with mites and/or lice. Mine had both. (Before I learned how awful pet stores are.)
She is twitching this way because it's painful for you to touch her. Even if you don't see itching or bald spots she most likely has mites or lice. Mites are microscopic and you cannot see them. Lice are tiny, wriggly, and white. Mange mites can be fatal and are very uncomfortable for guinea pigs.
She should be taken to an exotics vet. Don't let them do a skin scraping, they are useless and painful. She should be treated with nothing except Advantage, Ivermectin, or Revolution. Good luck, I've dealt with mites and lice and they are both such a pain but VERY common!
About the veggies, just keep putting them into her cage and eventually she will try them. She's much more likely to eat veggies if she has a friend, but please don't adopt one until the mites are gone! They are herd animals and should live with a friend at some point, though.
You aren't picking her up and you've had her for months?? Pick her up! They SHOULD be handled daily from the day you get them. She'll run and hide from your hand but just grab her and make sure you support her bottom.