Possibly the Tiffany Aching books by Pratchett.
a teenage or young adult fantasy.
Check, this was a young adult series Pratchett wrote taking place in his Discworld series.
Not sure if it the author was a man or a woman.
Terry is a first name used by both genders.
But pretty sure it was either 3 or 5 books in the series.
There are indeed five (although I think the final was posthumously published)
At least I'm sure it plays in medieval times.
Discworld until the last couple of books is pretty well rooted in medieval setting...ish.
It's about a young girl who has the power to see from others' eyes and even possess others, but it's dangerous and tiring for her to do so. I think it's dangerous because she might not be able to go back to herself again.
That is the Second book, Hat Full of Sky. The book starts with Tiffany going “borrowing” (seeing through another’s eyes) in order to see if her hat is on correctly. There is danger in borrowing, because one’s mind slowly changes to become that of the creature being borrowed. But also, as we learn, because you leave your body as a vessel, which can be invaded by other things. This is not a power unique to Tiffany, all the witches do it. But it is fairly unique in someone that young being able to do so.
I think she accidentally exposed her power in the beginning of the books,
but I know she, and others with the same gifts (there are not many) were feared by other people and were called something special (as a dirty word) because of that gift.
Her parents were dead, and I think she got the gift from her mother.
I think the idea from the first book was that her grandmother was a sort-of witch (not so much spells as the all-knowing matriarch who was the measure by which everyone and everything was measured). And thus she “inherited” her abilities from her grandmother.
The title of the book might have been the dirty word that the people with that gift are called.
Not so much. But Hat Full of Sky of course refers to her head being empty as she goes borrowing.
I remember her either fleeing from her town, or being kidnapped, because of her gift. I think she also had a brother (or a friend), with a similar or the same gift, and both were trying to find each other again.
There’s a lot of fleeing and a boy involved in the stories. Not on the nose here tho.
There might also have been a different language sometimes, I think I remember a cursive, bold font style in the books with that, but that might also have been when she saw through other people's/animals' eyes.
Usually the first person perspective of borrowing was written in an italic font. When the perspective changes to that of the Hive, I think the font also changed, but I don’t quite remember. Death also appears, as he does in every Discworld book, **AND TALKS IN ALL CAPS AND BOLDED. **
Sorry about the confusing and contradictory info, but it's been at least 10 years since I read the books and my memory sucks :/
Wee Free Men, the first book, was published in 2003, the sequel in 2004, and the third in 2006. So that would be right around the right time. The fourth way in 2010, so perhaps you became aware of it when the fourth was published.