Dylan–
Not 100% sure what you mean when you say “try to foam roll my quads”.
If you are not doing it correctly this could be the cause of some of the pain.
If you are very tight it is going to take time in the beginning for shorter periods of time.
Do a dose have time away and go back for another dose.
Pain is your body’s way of telling you something is wrong.
Have you had anyone video you squatting so you can see exactly what is happening?
Seeing it will help you identify what is happening.
How are your squat mechanics?
If you have an issue at the hip this could be an impacting factor for what you are experiencing when squatting.