booting up my Macbook using option key and power on results in white screen with mouse
Now that an external boot recovery or internal recovery is out of the question, you have two options. 


Try Internet recovery. Boot with option + command + R held 
Take this Mac to another Mac, use disk utility and run an installer over target disk mode
Find another Mac to make a recovery USB drive or bootable installer. Recovery is smaller and does less. Installer is larger and does everything the recovery does plus has the install package to reinstall the os. 


https://support.apple.com/en-us/HT201372 - bootable installer 
https://support.apple.com/en-us/HT202294 - recovery assistant



Internet recovery doesn't work on all older Mac hardware. Some protected wifi  / fire walled networks prevent internet recovery. It works in most home and public wifi situations quite well. Try that first. 

Target disk  varies depending on what specific Mac you have. Some work over USB, some work over FireWire, some work over thunderbolt, some work over more than one of the above.

The option of just making a bootable installer or a bootable recovery USB drive will always work assuming you pick the right version of macOS for your specific Mac.