"iPhone Unavailable"

My only option given on the screen now is to erase the phone

Correct

but I have thousands of pictures that are not on iCloud because my storage was full

This confirms that the pictures are only on your iPhone and not backed up elsewhere

Everything I've looked up already said that if it's not backed up then it's gone

Everything on the phone will be erased

but I don't want to believe that it's not possible somehow, even if I take it to Apple

Understandable, so you should take the Phone to Apple to have them confirm that what you are hoping for cannot be accomplished.

My phone still has notifications coming through constantly so how can my data be gone already?

The data is not gone now, but it will be when you erase the phone to reset it and set it up again.

Is it possible to back up my phone now while its disabled somehow? All I genuinely care about saving on that phone are my pictures.

No, it is not. But, you can have Apple confirm this when you take the phone to them.

All I genuinely care about saving on that phone are my pictures.

It is unfortunate that they will be lost.

If you enter the wrong passcode on your iPhone Lock Screen too many times, an alert lets you know that your iPhone is disabled. (Learn what to do if you see "[Device] unavailable" or "Security Lockout" on your iPhone or iPad.)