First off if I've been squatting really heavy for a while without much break I get a little knee "discomfort". Nothing major and certainly not enough to cause me any distress. Generally after I've taken a break from going really heavy for a little while my knees are good to go. But I'm old, btw. The point is that even having good form, a little wear and tear, and general discomfort goes with the territory.
But it sounds like you have a little injury brewing. It may not necessarily been cause by the squats. In general if you squat A2G and have good form, don't bounce, etc. it's good for your knees. It could be however that you are doing some things wrong. You have to take care that you knees don't come out way far over your toes at the bottom. It may not be possible for them not to come out a little but you need to be aware of this. Make sure you are squatting off your heals and not you toes. Make sure that your knees are in line with you toes. Try to sit back into the squat and then drive off of your heals using glute and ham action.
Make sure you go as low as possible (at least break parallel while maintaining neutral spine). One of the worst things you can do to your knees it to try to arrest the downward movement at some point rather than taking them through their range of motion. This will suddenly transfer the load to your knees.
But right now I think you need to take a break from it before you turn it into a permanent problem as the kind of pain you are getting is abnormal for sure. When they say no pain no gain that is not the kind of pain they are talking about..well, except for idiots
Read the injuries stiky to see if anything applies to you. If you only get pain on the squat and not in general just walking around you'll probably be ok. You'll need to take a break and get back into it with very light weights and concentrate on learning the movement while paying attention to your knees. Heavy and correct are mutually exclusive a lot of the time. You may have gone into the program too heavy.