Yesterday

I went to my friend’s house. I played with her baby! I enjoyed talking with her and taking pictures! I’m looking forward to see her again!

There is nothing grammatically incorrect here, but as a general rule of thumb, you want to avoid starting consecutive sentences with the exact same word.

One possible alternative:

"I went to my friends house and played with her baby. We had a great time talking and taking pictures together. Looking forward to seeing her again!"

On a side note, although it's clear from context that you enjoyed talking and taking pictures with your friend, strictly speaking, what you have written could also mean that you enjoyed talking and taking pictures with the baby.

Yesterday

I went to my friend’s house. I played with her baby! I enjoyed talking with her and taking pictures! I’m looking forward to seeing her again! モエコサンの文章は正しいです。 ”See" -> "seeing" "〜ing"はそれを初心者向けの動詞にします。"Seeing" means that you look forward to the experience of seeing her again.