Oh no, I feel your pain! It's possible for her to give you a second one but the chances are slim apparently! I've gotten second photos from Static and Muffy but they've been on my island since the beginning!
Sorry to hear that.
I'm always terrified about accidentally selling exclusive items at the cranny.
Villagers will give you extra photos but you'll just need to keep gifting her and putting in the same kind of effort you have...
Maybe consider posting about it and someone could sell it to you for some TBT or bells?