The idea was to see an orthodedist or maybe a podiatrist to rule out any structrural problems with the feet or what have you. For sure the lifting problems and that problem are two different issues so a doctor who doesn't specialize in sports or what have you would just be a base of information to work from.
But a lot of what doctors may call structural problems may not necessarily be congenital and stem from imbalances.
The problem with just trying to correct form is it's like asking a catepillar how it crawls. If your body is doing what it has to do through faciliatation or inhibition then you can think about it all you want but may not be able to overcome it. A person who overpronates will not necessarily be able to stop themselves from overpronating if they are not aware of the difference in the first place.
But of course you should start with being aware of proper form. You should try to push more though the heels and feel the weight over the middle of the foot rather than feeling a lot of pressure focused on one or two small parts of the foot. I don't know if that makes sense. It's hard to describe what it should be like just like it's hard for your to describe what it is like for you.
The knees should stay aligned with the feet and should not be turing inward.
Now you say you "push with your feet" and although it is important to try to drive through the heels and all that like I said before it may help you to think of it in a different way. My adage with squatting is to "relate to the bar, not to the floor". You are trying to move the bar up, not push the floor away from you! People tend to make it all about pushing downward through the knees.
Instead initiate the lift by pushing your shoulders and upper back up against the bar. In other words think simply about moving the bar up. What this will do is initiate the hips in coordination with the knee extension which is what you have to have. Believe me, this simple mental shift can make a huge differnce.
To check and work on your form you need a lighter weight. If the weight is too heavy then there is not much chance that your will be able to correct any form issues through will power alone. You need a weight that is heavy enough to necessitate proper form but not so heavy you can't do it correctly.
The thing about women and squats that doctor said is such ridiculous nonsense! Women will be MORE prone to knee problems from ANYTHING because of the alignment of the pelvis and knees. It has nothing to do with low center of gravity. For sure doctors, as I've said time and again, don't know any more than the average person about this stuff. It can be very frustrating.
If I had a dime for every moderately active woman I've known who's had knee surgery I'd have fifty cents
. Which is a lot if you think about it.