In this situation a brace/support would be well used to prevent further injury, but NOT to just help support the knee.
IE if your knee is moving over AND causing damage doing it, popping out of its track or becoming painful a support preventing it moving over is a great idea. If its not that bad then a support is simply stopping that inner quad muscle working as hard as it needs to, which isn't good when you want to strengthen it.
Static squats/most squats won't be particularly good, if you have muscle imbalance you don't want to do an exercise that strains the weaker and the opposite strong muscle the same, you want to hit the inner muscle as hard as possible and the outter as little as you can manage basically.
Some of the NHS physio's I've seen, and one/two private ones were, honestly, terrible, some of the ideas these guys have is laughable. Going to hugely better physio's and some of my many joint issues were solved very easily. I'd definately recommend trying a couple different physio's and essentially getting a second opinion.
Its also a real problem with doctors because some work with utterly awful physio's who think one problem will basically have to be fixed by some bodge job surgery, while another doctor works week in week out with the results from a truly fantastic physio and see's the same problems as easily fixable with exercise and no need for surgery. Theres very little in the way of consistancy in quality between physio's and treatments different doctors will recommend.