My guess is your issue is any one of the following.

• You are resting the bar too far forward. I see a lot of people in my gym with the bar resting almost on their neck. This is very dangerous and hard to watch. It should be resting across your rear deltoid. Refer to the picture in @BerinLoritsch's answer to this question for proper bar placement. It should feel too far back when you unrack it. It will then feel solid during the squat movement. I'd recommend throwing out the towel/padding. It is harder to feel where it is resting and can result in movement during the lift. If it is resting on your muscle you won't feel much discomfort.
• You are NOT leading with your butt. You need to actively lead the squat down with your butt with a pronounced arch in your lower back. On the way up you also need to lead with your bum. Don't let your back fall over on the way up. Keep a slight (15 degrees or so) lean forward but consciously keep yourself fairly upright as you stand up.

Make sure you use safety bars so that if the lift is failing, you can sit back down and let go of it. Do NOT lean forward and let it roll off your neck. You will do damage this way. In fact if your first instinct is to lean forward to dump the weight then you can be pretty sure the bar is too far forward. It should feel natural just to squat down and dump the weight on the safety bars.

Happy squatting.

My guess is your issue is any one of the following.

• You are resting the bar too far forward. I see a lot of people in my gym with the bar resting almost on their neck. This is very dangerous and hard to watch. It should be resting across your rear deltoid. Refer to the picture in @BerinLoritsch's answer to this question for proper bar placement. It should feel too far back when you unrack it. It will then feel solid during the squat movement. I'd recommend throwing out the towel/padding. It is harder to feel where it is resting and can result in movement during the lift. If it is resting on your muscle you won't feel much discomfort.
• You are NOT leading with your butt. You need to actively lead the squat down with your butt with a pronounced arch in your lower back. On the way up you also need to lead with your bum. Don't let your back fall over on the way up. Keep a slight (15 degrees or so) lean forward but consciously keep yourself fairly upright as you stand up.

Make sure you use safety bars so that if the lift is failing, you can sit back down and let go of it. Do NOT lean forward and let it roll off your neck. You will do damage this way. In fact if your first instinct is to lean forward to dump the weight then you can be pretty sure the bar is too far forward. It should feel natural just to squat down and dump the weight on the safety bars.

Happy squatting.