iPhone won't turn on !!!

Try a forced restart. As to whether you'll lose data, I can't tell you you will or won't. The time to ensure you don't lose data is long before something goes wrong. So if you do, this may be a painful lesson. BACKUP BACKUP BACKUP.

For iPhone 11:

1. Press and quickly release volume up button
2. Then press and quickly release volume down button
3. Then press and keep holding the side power button (keep holding past the swipe to power off) until you see the Apple Logo, then let go

See if your phone comes back up and hopefully no data loss. DO NOT TRY TO UPDATE UNTIL YOU'VE BACKED UP YOUR PHONE and then you will have to start deleting things you don't need or use like Photos, Apps, Music, Messages, Email, Files, etc., to ensure you have several GB of free space on the phone.

It appears you bought a phone which doesn't have enough memory to meet your needs. You should give consideration to a newer phone with more memory. Once purchased, there is no way to add memory as the physical memory on iPhone is fixed at purchase.

See this link on what to do if your phone is not recognized by your computer --> If your computer doesn't recognize your iPhone, iPad, or iPod - Apple Support

Little by little we'll whittle this away till you've got things sorted!

I believe the message you're seeing is not suggesting your iPhone is full. It is suggesting you need space on your computer.