Also Aya realized she messed up because she couldn't make a decision. So I think it is implied she would do it on her own at some time, had her mom not found that picture.
I mean, maybe? I felt like "it's time for me to put an end to this" sounded more like she was leaning towards cutting ties with Risa for good, giving them both a chance to move on. And the way she describes it to her mother - something in the past, before she got married, they broke up a long time ago - doesn't exactly contradict that. If she wanted to take this opportunity to come out for good, she could've said so. "We dated for a while, and I still have feelings for her" would be active, ongoing, motivated, but instead, she made it easy for her mother to interpret it as a phase she went through, before she got serious and married a guy.
Not that there isn't room to read this optimistically, but I don't think we're given the tools to suggest that Aya has that kind of resolve. She's a weak person, and that's fine, but I would've liked to see her become stronger before she jumped back into a relationship with the woman she's strung along for years. Maybe their story isn't over yet, and that's why this part was so easy - the author still intends to show her struggling with the relationship, but this time, she won't give up. I kinda hope that's the case. As it is, she doesn't inspire much confidence.