??

Some profiles are glitched, simple as that. You library has the correct number.

When you add a non-steam game to your library, it bumps up your number of games (it counts the local non-steam ones too), but it doesn't do it on your online profile.
For example: I have 229 games is my library, but only 225 on steam.
Also can be a bug, as others stated above.

Please open Internet Explorer, Safari or Firefox and type steam://flushconfig then press Enter. (If asked to allow this website to open a program, please click 'Allow' or 'OK')

When prompted by Steam to reset your configuration, please click 'OK' to confirm.

Once done, login to Steam and re-test the issue.

If you have multiple installation folders for games doing this process will remove them. You will need to add the folders again in Steam so that your games will appear as installed.

In order to add the folders please do the following:

1. Open Steam
2. Click Steam > Settings (Preferences on Mac)
3. Navigate to the 'Downloads' tab
4. Click the 'Steam Library Folders' button
5. Click on 'Add Library Folder' and add the directory that contains your games
6. Click 'OK'
7. Restart Steam

If the issue persists, make sure your network is optimized for Steam:

Please follow all suggestions in this article, even if your network appears to be functioning correctly.

I redeemed a steam code and it went up to 110 games.

nah.

All the free games will show up on your Profile as games if you ever played them showing the playtime it's normal also often dlc's.

Those are free 2 play games. After you uninstall them they remain in your steam account but not in your library.
I got 242 games in my library and 244 games on my steam profile (ABP Reloaded and Spiral Knights).
Hope this helped you.