Whenever I'm driving let's say... 60 mph and I try to come to a complete stop, I press on the brake them BAM the problem starts. Whenever I press on the brake, even slightly my truck rocks back and forth while moving down the road. It's bothering me badly so if anyone has a solution I'm all ears.

 

Do you have really badly warped rotors?
You can test it on a smooth section of street at about 25 MPH.
Just apply the brakes very lightly. You are looking for surging as the warped section drags on the caliper. It will feel a bit like you are riding a camel. At freeway speeds it feels more like a shudder.

 

I'd keep off the road if possible, sounds dangerous. Jack it up grab wheel at 6 and 12 and wiggle it around, checking for worn hubs and ball joints. Do same grabbing at 3 and 9. If that feels good get the wheel off and inspect brakes. Broken bolt, pad, etc. If in doubt get some pics, put them online somewhere and post the link here so we can check it out.

 

Like David said need to check front end parts, tie rod ends, ball joints etc. While you have the tires off the ground use a crow bar or similar placed under the tire. Have someone lift and lower the tire while watching the ball joints.