Blown shock would leak fluid. Hard to imagine it would have visible damage unless you collided something and straight up smashed the car.
Pulling to one side during braking could be alignment or brakes. Alignment will require a shop. You said the tires look good at all 4 corners?
Its also possible that a fitting or a line has broken at one corner of your brakes. Look for anything obviously hanging off the car (unlikely, unless direct impact or poor work by prior mechanic). Also bleed the brakes and see if there's any issues at one corner.
38k km doesn't seem like enough miles to just be mere wear on a suspension arm or joint
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