Asymmetry --> broken body:
Naim Suleymanoglu - 1996 Atlanta World Record - YouTube
So far all of the tips given are worth considering imo.
Just keep in mind that yes, squats are hard and uncomfortable, but in your situation, there is no sense in being fearful under the bar und your form adjusting to the weight: you adjust the weight to allow good form and THEN challenge your body to keep that form with progressing weights. You should succeed in that in more than 90% of your reps - not in one out of five.
There is a difference between a large structural anomaly that inevitably leads to greatly altered (individual) form and largely functional altered form (based on small structural anomalies). What weve known so far, you dont have the former one (5mm leg discrepancy is pretty much normal). So prevent your body from escaping the hard, but correct form. Btw thats exactly what happened to Naim in the video above - only that it might be worth allowing it at a world record attempt at the Olympics when going for gold...
You need practice, self-confidence, automatism and strength with good form. You can only achieve that by that squatting with good form regardless how much less weight on the bar that means at first.
Form --> weight. Not vice versa.
As for the rate of progress: Technique will be a major factor, and you probably will find something to improve in the other areas (nutrition, recovery) as well. Dont compare to others.