You tagged this question about qt, which is a tag I follow. However, you are also asking with regards to c programming.
If for some strange (or domain-enforced) reason you feel you must use C and not C++, then Qt is not for you. It was designed from the ground-up as a C++ library.
Yet I'd strongly suggest questioning why your project would need to be in C. There are many benefits to C++, and the idea that C performs intrinsically better is mostly a myth. For some hard data on that, check out Bjarne Stroustrup's Learning C++ as a New Language.
If you must stick to C then there's always GTK. The underlying API of GTK+ is C, but bindings also exist for C++ called GTKmm. I'm not a big fan of it from a design perspective, but historically powered the Gnome desktop (Ubuntu's default)...and Google chose it for their version of Chrome for Linux. So it has some cred and support there.
But do note that Ubuntu is choosing Qt5 to implement their next version of "Unity" in the desktop:
https://askubuntu.com/questions/281092/why-is-canonical-choosing-qt-over-gtk-for-unitys-next-generation
EDIT: You added:
If I must use C++, that's also fine.
"Must" is a strong word, but there is practically no comparison between C++/Qt vs. C/GTK. And the latter is becoming a thing of history.
