In the opinion of the FSF, you could only distribute your software under the terms of the GPL. Your software as a whole includes the GPL-covered library and is thus derived from the library.
The GPL triggers conditions both on modification and on distribution. But modification is not just about editing the library's source code. The GPL-3.0 defines:
To “modify” a work means to copy from or adapt all or part of the work in a fashion requiring copyright permission, other than the making of an exact copy. The resulting work is called a “modified version” of the earlier work or a work “based on” the earlier work.
Your software can be considered to be a work based on the GPL-covered library and is, for all practical purposes, a modification.
There have been lengthy debates over whether this argument still holds if the library is dynamically linked, or if the software is not compiled. There are people who argue that the GPL might not apply to your program. But it's safer to assume that the GPL does in fact apply.
If the GPL applies to your software as a whole, this doesn't mean that every component must use the GPL license. Components could also use compatible licenses. So you wouldn't have to license your source code under the GPL terms, and could instead choose a compatible open source license.