This is Pigs Don't Fly by Mary Brown, the second book in the Pigs Don't Fly series.
"I was a huge lump of grease, wobbling from foot to foot like ill-set aspic," confesses Summerdai, the heroine of this improbable charmer with the equally improbable title. Because of her girth, the 17-year-old Summer was passed over to replace her mother as the town prostitute. Equipped with a few supplies, a small dowry and a rather ugly ring left by her mysterious father, she sets out. But the ring is actually a bit of unicorn horn that warns her of danger and, most importantly, allows her to communicate with animals. In quick succession she picks up a ratty dog; a badly used horse; a starved turtle; a wounded pigeon; a man who lost both sight and memory after a bump on the head; and a rather curious little pig with tiny bat wings. The seven of them head south to look for the homes of horse, pigeon and man, during which Summer gains much self-confidence and loses much weight while the small pig/bat gets larger, wiser, more mysterious and more lovable.
When her mother, a medieval village whore, dies, Summer is put out of
her home so as not to become a "burden on the parish." With only a few
coins for her dowry and a ring as relic of the father she never knew,
the girl sets out to make her way in the world. The ring enables her
to converse with animals, and as she travels she collects various
strays, including a mongrel dog, a lost horse, a broken-winged
messenger pigeon, a tortoise, and a strange, winged pig. She also
rescues a blind and amnesiac knight. While searching for her charges'
homes, Summer names and nurtures them and with them encounters good
and bad people and a dangerous ghost. Although their homecomings are
not as perfect as she would have liked, most of Summer's friends
eventually have them. After the pig's dramatic transformation, Summer
is left to face life alone. Yet she has grown from a self-described
"fit and ugly" child into a slim, beautiful, and capable woman.