iPhone 11 Pro Max Boot Loop no storage for update.

Hi, today my apps started randomly crashing and slowing down so I decided to turn my phone off and on again to see if that would fix the issue.

Upon doing so, my phone wouldn't boot back up and began being stuck in a boot up loop where it shows only the apple logo on the black screen. It's been doing this for hours now.

I've tried hard resetting it by pressing up and down volume buttons then the power button, as well as doing the same thing whilst connected to my PC.

At times it does connect to itunes and itunes recognises that there is an error with the phone.

It tells me that the only options I have are to update to the latest ios 14 or restore the phone entirely.

My dilemma is that I hadn't backed up my phone since I've had it, my fault at that I know.

I have extremely sentimental data on my phone and absolutely refuse to lose any of it.

I tried to update the phone to the new ios to see if it iwould work but it failed halfway through saying that I did not have enough storage to complete the update.

is there any possible thing I can do from here?