whenever I make paneer, it is somewhat sticky on the teeth and doesn't give that 'squeaky' feel. I use the packaged pasteurized full cream milk.
You probably need a (small) cheese press and a proper cheese cloth. My attempts to improvise using chopping boards never drained well enough giving the effect you describe. It also doesn't brown nicely when you cook it, if it's too wet. When properly pressed it will cut into better pieces.
You also need to press with some force for quite a while. Recipes can be optimistic (or assume better quality equipment than I have).