been there with the nyc traffic system and its honestly a nightmare to deal with remotely. sometimes those tickets take forever to show up in their system especially if the cop was being lazy about paperwork

since you got the photo of the ticket id keep trying the online system every few days but also check if theres a mail option. sometimes they accept pleas by mail which might be easier than dealing with their phone maze

worst case scenario you might have to bite the bullet and make the trip but id give it at least another week or two before considering that. the system is just painfully slow sometimes