When my muscles are sore, I find myself squeezing the muscles just to get them to move ie, I'm squeezing my arm muscles that are sore while trying to raise my arm. Is this normal? Is it bad for my muscles since they aren't getting a "break?"

Not sure what you are talking about here.

Are you squeezing as in massaging the muscle? If so, it can't hurt and may help break up some of the adhesions that form as your muscles repair from the stress. Sort of like using "the stick" or a foam roller which are actually better than just rubbing and squeezing as you can apply more force and help break up the knots. This is known as self-myofascial release.

or are you squeezing as in flexing the muscle as in doing a resistanceless bicep curl for your arm. If so, this is pumping blood into the muscle which helps deliver oxygen to the muscle which will actually help speed the recovery process. You have the give the muscle a rest from a significant stress (such as your training) but this flexing or some very light resistance work actually serves as active recovery.

Or

Are you squeezing the muscle to try to get it to activate because you cannot raise your arm without this assistance. If this is the case, no it's not normal and yes it is a sign that you overstressed it or injured. Let it rest and have it looked at if it persists.

Or

If it is none of the above, then try to clarify.

I think that may be it but I can't recall what it was. After stretching just now, all my sore muscles feel better. I think I may go stretch more and see if that helps more.

Can't hurt. Are you already stretching at the end of your workout? If not, you should include a little into your cooldown. It sounds like you just overdid it a bit. Dial back the intensity a tad.

I do usually but it probably won't hurt to stretch more.