Do some doctors use instruments to determine dilation when you are in labour? My MD and the delivery nurses would check me once or twice during both of my labours so far with their hand - sterile glove on, lubricant, and a quick check with the fingers to feel how far dilated I was. Never hurt a bit, and I was always thrilled to hear when I was making progress that could be measured with numbers. But I have heard of others who find internals uncomfortable.
I believe you can check to see if you are dilated at home if you CAREFULLY clean your hand, and insert a couple of fingers to see if you can feel how far "open" the cervix is. I think you would feel kind of a ring with a dip in the middle. The dip is the opening. If it is big enough for a finger tip, you are about 1cm, two full fingers, 2-3 cm, etc. (It's been a long time since I checked my textbooks on that, but I think that's how it went. I'm sure someone more experienced could set me straight.)
As the PP mentioned, I wouldn't use that alone to determine how well your labour has progressed, or when to go to the hospital. Things can change pretty quickly, and how you feel with your contractions is a better indication, but I understand the desire to know if things are progressing "down there" or not. I certainly was curious, but I didn't know I could check myself.
And I believe you can refuse an internal in the hospital if you so desire, but I think they can provide helpful information to your care giver about the progress of your labour, the descent of baby's head, etc. Do your research and make an informed decision.
All the best!