I had to do a factory reset on my phone due to network issues. Before doing so, my network provider had me back up the phone, as well as a Google back up. Everything was completed before we did the reset. Once I reset the phone, the network issues were fixed, however I lost TWO YEARS worth of pictures and videos from the phone's gallery. I found out of course afterwards, that gallery is NOT backed up unless it is uploaded to Google pictures (which is a separate app that I DO NOT USE since I don't want all of my pictures on Google) or the Samsung Cloud. I had things on Samsung Cloud, but did not pay for the extra space that I should not have to pay for as a back up, but NONE of my photos. There needs to be a way for the gallery to be automatically part of the back up. Especially since I am not a huge social media person and keep most of my things for my own use. I lost photos of my nieces and nephews birthdays, pictures with other family and friends that I will never be able to get back and I am currrently devastated about it.
I am so sorry to hear about your lost pictures. I have had this happen to me as well and it's devastating. I understand not wanting to put your information on the cloud.
Another option would be to use a Micro SD card if your phone allows it. You can set your photos to auto-save on the card. Also, if you ever have this happen again you can save all information onto the SD card via the smart switch app.
I'm sorry to hear that you lost all those photos. Without the use of a cloud storage, you would need to back up your photos either to an external storage/hard drives or to a PC/Laptop using apps like Samsung Smart Switch. I've provided some links that show ways to back up without using a cloud storage.
Hope this helps!