What does it say when you just click on "This PC"? You should have all drives listed there with the space used on each of them. Your C should be almost empty. If one of the drives is full that would tell us something (again, I find it suspicious that Nvidia driver setup says there is no space left).
You could also open a task manager and look at the memory usage. If it's close to 100% that would explain why Nvidia setup also said you could be running out of memory. With 16 GB you should not be using more than 20-30% at idle (likely even less if you have a fresh install without any app running in background).
If neither drive is full and you have enough available RAM, I would personally physically unplug the HDD and reinstall Windows on the SSD. There could be still a boot partition on the HDD from the old Windows installation that is messing things up. If your Windows is still clunky after a reinstall on the SSD without the HDD connected, then there could be something wrong with the SSD, the RAM, the MB or the CPU.