When shaking it in and out, look at the tie rod ends, the thread part of it. If the threaded portion is slipping in/out that's when you know you have a bad tie-rod. Check out the bushings and see if they are corroded. Honestly, only experience will teach you to spot things like bad suspension components, so I'd recommend you to get a friend or someone who has experience diagnosing stuff. Its hard to help without actually looking at it.

Also, I wouldnt be completely shocked if your axles took a shit again, especially if they're refurbished ones.

I dont know why people never realize this, but many shops will check it out for you free of charge. As someone mentioned, Aamco will do a free inspection. I ussually go to a shop first, regardless of knowing the problem or not and then fix it, if I can.