The wheel shakes when the car is around 55mph but goes away as I hit 60-65 mph. I noticed it happens mostly when the wheel is turned slight left too and not as much when it's turned right.

Does it need to be balanced/aligned? I had discount tired do it because I complained about it earlier and I'm thinking they didn't do it properly.

 

I'd first make sure you have no loose front end components. They should be checked AT RIDE HEIGHT, not with the suspension hanging down (like on a frame hoist). The idea is to check at the position they are in most of the time. A tie rod end can feel fine with the suspension extended but actually be loose at ride height for example. An alignment rack with turn plates is the ideal way to check.

Beyond that, find a shop that can road force balance the tires. Even if they are dynamically in balance unloaded, there can still be road force imbalance when the tire is actually on the road with weight on it. I cured quite a few hard to find vibration problems with the road force balancing over the years. Most times (not always though) if a shake happens in only one speed range it points to road force imbalance. The A4's had that problem in '09 and it was a steering wheel shake from 40-45 mph. Below that speed was fine, above was fine and road force balance helped a ton (so did the new lower links also, in the TSB).

You may also want to run the car with the tires off the ground to make sure they run straight and have no wobble. A hub with too much lateral runout can cause a wobble same as a bent wheel.

Vibration/shake diagnosis is a procedure and just start with the easiest and work your way up from there until the problem is found.

 

Kudos to you for a well thought out, logical, and meaningful reply.