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*a whole month* after you got your tires changed is kind of inconclusive on that part, but it's not impossible that while you had the tire change and the wheel was off the hub, some rust (Your location: Canada) can fall between the hub and rotor if it's moved, making the rotor run as if warped once the wheel is put back on, which would also run with a slight wobble.
Again: Your location being Canada (or anyplace above the US rust best really) a rust ridge at the inner outside edge of the rotor is a common cause of cyclic metallic rubbing noises coming from wheel and brake area if that ridge is large enough to contact the backing plate, which itself might have gotten pushed towards the rotor by rust over the years. A rust ridge can also cause brake squeal, as instead of running on a flat rotor, your pads now run in a V groove (with a really wide and flat bottom) which can cause them to squeal like a V belt.
Of course your brakes could just be at the wear limit and the squeal you hear is the wear indicator doing it's job.
Also, that doesn't explain your handling concern, but it doesn't have to: Your car is a 2015, a worn suspension component isn't out of the question. "A mind of it's own" handling, in my experience, is often caused by REAR components being worn, you may have a worn joint on a toe link or control arm. I usually test for this on a flat piece of highway that has nice ruts from heavy truck traffic. On a slow lane change, the ruts will load the suspension side to side and the rear will feel like it wants to change lanes faster than the front.
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