Hello! To answer your question "a photo shot by me" is correct. You could also say "a photo taken by me". Since "taking" is present tense, it's normally only used as you are taking the photo. Taken is the past tense.

It would be more natural to say "A photo taken by me" or "A photo I took". However, since you're posting the picture and it seems like that will be the caption, it's more natural to just say "Taken by me". After all, the photo will be right up there; people will be able to tell that it's a photo.