Just some random thoughts:
I don't see how not having squat shoes would cause injury, and see plenty of people squat in all manner of footwear without injury. I also doubt that getting good squat shoes will cure what's ailing your knee.
So what is ailing your knee? Well, we can only guess without a form video. How could we know if its a stability issue with the feet? Do you feel stable or no while squatting?
In my limited experience in regards to self-approving form, "don't we all" really fits the bill. We almost always think our form is better than it is. So with that in mind, I'd say your issue is probably form-related. BTW, I have nothing against squat shoes, they've really helped me out with depth. But I don't see them as doing much to prevent injury.