For uninstalling Qt 3, first try to find all installed rpms of Qt 3. You can use the following command to find Qt 3 rpms:

$ rpm -qa |grep -i qt
This will list all Qt rpms. Then you can use rpm -e option to uninstall the rpms.

For installing Qt 4.4.3, try to find a compile version of Qt from the internet. But it might be difficult to get a compiled version since you are using an old kernel and possibly a old version of Linux.

If you want to build it from source, then following the commands given below:

$ tar -xvf qt-x11-opensource-src-4.4.3.tar
Thi will create a folder named qt-x11-*

$ cd qt-x11*
$ ./configure
$ make
$ sudo make install

You might get some errors during configure or make. If you get any errors, it would be because of missing dependencies. So, you'll have to install the dependencies first and then try compilating Qt again.