Lots of misunderstanding of copyright law in this thread! I don't have time to address everything, but to answer the OP's question:
If your contributions to the songs were significant enough to make you a co-author -- e.g., you came up with portions of the melody or lyrics -- then you and the other guy are joint owners of the copyright and can both use the song. You don't need to get each other's permission, but you do need to account to each other if you make any money from the song.
If the other guy wrote the song and you just came up with some accompaniment, you can't use the song, but you can re-use your parts in a different song, assuming your parts do not infringe his composition by copying the melody, etc.
Note that the above addresses the copyright in the songs themselves -- i.e., the compositions. There is a separate copyright in the recordings that you made. If you both contributed to creating the recording, then you are co-owners of it and either of you can use it. Again, you would need to account to each other for money you make from selling the recording. And the other guy may be entitled to additional mechanical royalties for his song if you sell copies of the recording.