1993 Toyota Corolla Vibration on steering wheel

Hi, I have a 93 Toyota Corolla automatic transmission, 2 wheel drive and 1.6 engine with 180,000 miles. A week ago, I personally changed the both front struts and coil springs since the front right side coil spring was broken making the car leaning to the right side, and I was sometimes getting a shimmy steering wheel when I push the gas pedal only between 25-50mph. Now I am having shimmy steering wheel all the time between 20-40 mph. This only happens when I push the gas pedal and disappears when I lift my foot from gas pedal (without pushing the break pedal). Sometimes, I let the car go without pushing the gas pedal or pushing it enough to keep it moving and when it gets to 35 mph I push the gas pedal and the car runs fine without any problem.
One mechanic told me that I have to change the front left axle and another that I have to change to spark plug wires, distributor cap and rotor. Now I am confused. Can you help me.
Do you think this can happen because the struts and coil springs were badly install. Does it has to
do with the axle or CV joints. I will really appreciate your help if you can help me. Do you have any idea what it can be.