I have a new iPhone 7plus. My 17 year old helped back up my old iPhone before we left on vacation last week. My new phone was activated but not synced before we left. When we got back, I asked him to sync my phone thinking that still needed to happen. Well, it erased all my pictures from our trip and took my phone back to the backup before Spring Break. I have called Apple and an independent company and told there might be a tiny bit of hope in something on my phone called TRIM. I am obviously not technical and have no idea what this is. Any help is appreciated. Is there any possibility in retrieving my pictures or not?
Regrettably TRIM is unlikely to be relevant to recovering your lost photos.
A trim command (known as TRIM in the ATA command set, and UNMAP in the SCSI command set) allows an operating system to inform a solid-state drive (SSD) which blocks of data are no longer considered in use and can be wiped internally.
However, a data recovery organisation may still be able to extract photos from your iPhone's storage. Much depends on if the location on the storage has been erased or if the original files are encrypted.
The technical details of how your photos could be recovered is better left unknown; it is unlikely to directly help you. Contact a couple of reputable data recovery organisations and ask them for quotes.
This is a horrible situation to be in. I hope you are able to recover the photos. Good luck!