Hi! I need to buy storage for my iPhone but from my computer. my phone won't turn on.

Your post is a bit confusing.

1. Restoration does not require any free space on the iPhone.
2. iCloud storage is separate and independent of your phone's storage and buying more of it, will not increase your iPhone's local capacity.
3. Restoring by definition will wipe the iPhone clean so all data will be lost. Unless you have an iCloud or iTunes backup, there is no way now to recover your data. Your data on the iPhone is already lost at this point.
4. You can try to reboot your iPhone and see if it will correctly boot up by following the steps here: link-> If your iPhone, iPad, or iPod touch won't turn on or is frozen - Apple Support
   1. This will not delete your data from the iPhone, but may not let you access it wither if it cannot correctly reboot.
5. If the previous option does not work, then you will need to restore the iPhone as explained here: link-> If you see the Restore screen on your iPhone, iPad, or iPod touch - Apple Support

Restoring the iPhone will delete all data from the iPhone. If you don't have a backup, there will be no way to get it back.

So my iPhone show the apple logo idk what do I do