Do you class your c-section as giving birth? (seeing as that was your original question)

Clearly you do. So then, you gave birth to Amelia.

Pretty simple.

However, if someone came to me and said "i had a horrible c-sect experience, and i really don't feel like a gave birth and i find it hard to say I gave birth" then i could easily sympathise with that mother and let her know she's not alone feeling like that sometimes and that there are proper professionals out there that can help her feel differently or come to peace with her birth experience.

How you feel is what matters. And if you feel great, then someone elses comment doesn't affect you. If you feel terrible and you are hurting then it's legitimate too.