Thank you for helping a dog in need!
My dog was an emotional wreck when we first got her. She was too thin and had been physically abused. She was terrified of men including my husband and son. Walking her on a leash helped a lot. She quickly realized that she could rely on me to look after her needs and protect her. I kept increasing the length of our walks as she became more confident.
Keep in mind, my dog never threatens to bite when she is afraid. Instead she will cower away and hide or roll over to show submission. If your dog is a fear biter, it is best to keep a muzzle on while walking/interacting with socialized dogs.
She warmed up to my family with some time and patience. Now adores our son and is her daddy's little girl too. When she meets a strange man, she sometimes still hesitates. She will look to us for cues.
Walking also helped because we live in a very out-going neighborhood. We often cross paths with another friendly leash-walker whose butt desperately needs sniffing. Men walking nice dogs are apparently a step up from a male stranger without one. She is usually surprisingly friendly.
Now she has quite a few good doggy friends who we socialize with on walks, at the bark-park, and on special play dates. Some of her doggy friends have stayed at our house when their owners needed to go out of town. She still has lapses when she will flinch if someone reaches out too quickly, but on the whole has come a long way.
So long as the vet has cleared her, the trouble keeping her food down could be nerves or a shrunken stomach. Try more small meals instead of big ones. Also try feeding her somewhere she feels calm and safe.
Good luck finding the right solution for socializing your dog. They can be the best of companions and all deserve healthy, loving homes.