I made a material, but I do not need it on the entire model, so I wanted to know if there was a way to paint the material on only part of the model.
Not directly, you can use a black and white texture (using texture paint or vertex paint on the model) so black is one material and white is another material. Grey is a mix of the two.
You way you set this up depends on the renderer you are using and your model, neither of which you have supplied any info on.
You can mix cycles materials using vertex paint. Copy my node setup (ensuring that your attribute node has the correct name “Col”) - then go into vertex paint mode and paint some of the vertices on your object black - you’ll see that the black parts have the diffuse blue material - whilst the white parts have the glossy red. You can use this for mixing any materials.