There are several ways to transfer files between an iOS device and a PC for free.
Cloud storage like iCloud, OneDrive, DropBox, etc.; with these services, there is a “free tier” where you have a specified amount of storage space, usually 5GB.
If it must be completely free, you can sync files 5GB a time. Files are copied to the shared folder, sync’ed, between the cloud, the device and your PC, then moved from the PC’s sync’ed folder to another one that’s s not synced.
If you are willing to spend $1 with Apple, you can do this at 50GB a time For $2 with OneDrive you can do this at 100GB at a time. Simply cancel the upgraded storage at then end of the month.
SMB file sharing. You didn’t mention which OS you’re using on your PC, so assuming Windows, you can use file sharing to create a shared folder on the PC then with the native Files App, connect to that share and copy the files over.
Free file sync apps like GoodSync Explorer. There are many different ones, I selected this particular one for the high ratings and the fact it can turn your iOS device into a “server” and you can access your files via a web browser. I’m not affiliated not have I used it personally (no need)
With a little creativity and patience, you can transfer your files via WiFi. As for “free apps” like GoodSync, I’m not a fan because nothing is free; or more colloquially, there’s no such thing as a free lunch. What are you giving up to in exchange for that developer creating a program? Usually it’s your private data. Personally, I would spend a few dollars to do this securely and conveniently.
Now all that said, how “overloaded” is this PC that iTunes won’t load but your willing to store your data on it? I suggest attending to that PC first, then using iTunes, sync your filed via USB because it’s significantly faster and more reliable. I say this, because it sounds like you’re not backing up your iPhone at all and you should be backing it up in some way.