Welcome to the forum Cody! I haven't used Music Manager since shortly after it was first released, so I'm not sure if that functionality exists now, but I know it didn't. From what I recall, it was basically a barebones way to upload your music to the cloud and then you can create playlists and such from there.
When you say you made playlists on your phone, was that before or after you uploaded your music?
Do you have an All Access subscription, or are you only working with your own uploaded music?
I have All Access, so our results may be different, but if your music was uploaded before you made the playlists, the songs should be in there. When I create a playlist, whether on the computer or on the phone, the songs in the playlist sync with the names, which I would think should work the same whether you have All Access or not.
However, if you made the playlists before the songs were uploaded, that could be the problem and you may have to add the songs back in, but if you created the playlists using the Play Music app on your phone, there may be a way to sync them. How long has it been since you finished uploading and what's the approximate size of your collection? (How many songs have you uploaded, and did you upload all of them just now, or have they been there for a day or more?)