Do you have a backup of that prior install? My instincts tells me no, as a knowledgeable computer user would go there first. But thought I'd ask anyway, just to cover the bases.
There are tools, some of which are free, may be of help. Paragon & Mini Tool Partition Wizard Home Edition has recovery tools. There is also an app called Recuva, by the writers of CCleaner, that can find files for you, provided that they weren't overwritten.
What you can do is the shrink the partition back to 100GB, using the same tool that you have shown above. Right click onto the 120GB partition (after defragging), you should be able to restore that partition to the size that it was. Then, using Mini Tool Partition Wizard Home Edition, you may be able to find your lost partition, and recover your files.
This is why I always stress to backup (especially your data). And items of utmost importance I keep on 2 places, the data partition & a USB Flash drive or CD/DVD, in addition to backup. Macrium Reflect is very good, and free, so is Todo Free. The difference between the two is that Todo does data backups, while Macrium doesn't (the free version). But it will backup the data if it's own a separate partition.
Perhaps another member has other ideas, this is the best that I can offer. But whatever you do, don't overwrite that space that your data was on any further, as the more it's overwritten, the less the chance of any recovery.
Best of Luck,
Cat
