Hi Ron,
Seems like you are asking a couple of different questions. If a track got forwarded but you never heard from the library or signed a deal, then you should absolutely feel free to keep shopping it around
However, if you signed a deal with a library, you need to look closely at the terms of the deal for the track in question. If it was a non-exclusive deal, you could submit it to another library, but *only* to another non-exclusive library. In other words, if a track is signed with a non-exclusive library, an exclusive library can't and won't take it.
If you signed an exclusive deal, you'd need to look at the terms. Sometimes there's a time limit on the deal (5 years etc) after which you can pull it from that library. However, keep in mind that some exclusive libraries don't want tracks that have EVER been signed elsewhere, because they can't guarantee where that track might be floating around having been used. Also, many exclusive libraries sign deals in perpetuity, meaning that track is theirs forever.
My suggestion? Write a new track of the same style and shop it around, and forget that original track exists
