Ivyblossom
Nice, not many people use Ivy or -blossom
56 moons
Not too young and not too old
She-cat
It's fine
Tawny pelt with green eyes
I like how you used tawny instead of tortoiseshell or dappled
Sweet, caring, courageous, loyal, over protected
Maybe add some flaws to even it out
Shadowclan
Not my favorite clan but I'm not judging you on that
Medicine cat
We don't get a lot of medicine cats
None
Good
Haronflight (deceased)
I'm sorry for your loss
Blackkit, Darkkit, and Fallowkit (she gave them to a she-cat who had kits the same day as herself)
Forbidden but at least she didn't make a huge deal about it
When her mother risked her life for her, knowing it would be her last days because she was old, Ivypaw grieved for days. She was supposed to be a warrior, but kept having dreams about a line of words, kin against kin, friend against friend, enemies will tear you from the inside out. She realized what it was and told the medicine cat, Clearwater. She trained as a medicine cat and when her mentor passed away (refused to go to the elder's den) she took over. (She eventually dies of green cough because she had no catmint and her apprentice takes over as Eagleflight).
There's a bit of gaps in it. What was her kithood or apprenticeship like. What did the prophecy mean.

In all this is a well though out character. Just add some flaws and fix a few gaps in the backstory but otherwise she's fine.
17/20