Restart on password unlock?
If I turn off my phone for a few days, would it somehow restart the
  password count and I could try a few more times?.


In a word, no. You can try restoring your phone to factory settings using these steps at Apple Support.

If you backed up your device, you can restore your data and settings after restoring your device. If you never backed up your device before you forgot your passcode, you won't be able to save the data on your device. 

Quoth Apple:


If you don't have iTunes, download and install iTunes on your Mac or PC. If you don't have a computer, borrow one from a friend, or go to an Apple Retail Store or Apple Authorized Service Provider.
Make sure that your device isn't connected to your computer, then choose your device below and follow the steps: 


iPhone 6s or earlier, iPod touch (6th generation or earlier), or iPad with Home button: Press and hold the Side (or Top) button until the power off slider appears.
Drag the slider to turn off your device. Connect your device to your computer while holding the Home button.
Keep holding the Home button until you see the recovery-mode screen.

In iTunes, when you see the option to Restore or Update, choose Restore. iTunes will download software for your device. If it takes more than 15 minutes, your device will exit recovery mode and you'll need to repeat steps 2-4.
Wait for the process to finish. Then you can set up and use your device.