I'm glad that you got a chance to do some free weight squats! You can really feel them the next day...but the 2nd day after...will be worse!!! I feel it a lot in my "teardrop" - vastus medialis.
If the weight is too heavy and I'm already fatigued, I tend to lean forward too. Imagine yourself sitting down as you are squatting, that may help you stay more straight up. Also look straight ahead or up slightly.
Squats hit a lot more than your quads - hammies, spinal erectors, glutes, etc. so you may not get a huge quad pump. To emphasize the quads, drop the weight and do narrow stance with the bar fairly high on your traps.
Keep the "real" squats in your routine, just don't try more weight than your ready to handle. :squat: