Driver side wheel squealing while driving

Always lightly driven, no real hard accelerations or braking. About a year ago, my driver's side wheel started squeaking intermittently (I had new brakes and rotors put on for the first time about six months prior). It would squeak when driving slowly and stop when I hit the brakes. I took it into the shop a few months later and asked about it, and they said the brakes were not Toyota brakes, so they were just going to squeak. I have started driving more lately, and have now noticed that it is squealing when I drive at high speeds and turn the wheel very slightly. I took it to another place, and they inspected the brakes and said that they could change them, but there was not anything wrong with them and they were still at half-life. Yesterday, I was driving, and the noise became constant, at just about any speed, unless I hit the brakes. Could this be the brakes, or is it something mechanical, like a part of the wheel? One other thing I have noticed is that when braking, I am now feeling a pulsing or pushing in the car, like I am hitting the brake and something is still pushing forward. Are these things related, two separate problems? I know nothing about cars and do not have money to keep going to the shop, but I need this fixed, since my secondary source of income is driving. Any advice is appreciated.