2001 Chevy Silverado na

Possible transmission problem. It sounds like it's not downshifting everytime and you're starting off in 2nd or high gear. It'll feel super sluggish if this happens. There are solenoids in the transmission that control this. One could be sticking and preventing it from downshifting. They're pretty simple to replace if you determine this is the cause. Are there any codes? Check engine light?

Try to better describe what's happening. I'm gonna try my best to help you. When you say "dragging from the rear" what exactly do you mean? Like you're pulling something? Or do you hear something abnormal? I keep re-reading your question and still, the first thing coming to mind is the transmission is NOT downshifting. Try this: Next time it does it, if you're going slow (like leaving a traffic light) pull the shifter down to LOW or 1st gear manually. See if it will make a difference. Get back with me and let me know how that test went.

Well, manually shifting to LOW doesn't always override the problem. You still could have a transmission problem, BUT. You feel a vibration. This could be a shudder from the transmission or, what you said, the rear end failing. I would tend to think if the rear end was failing, it wouldn't straighten up. So, I'm still leaning towards the transmission. Can you drive a standard? Have you ever tried to start off in too high a gear? Or shift to a high gear too soon and lug the engine? You feel a little shudder/shake/jerk. Similar(but not exactly the same) things happen when you do an automatic that way. It's trying hard to go but the gear ratio is too high so you lose torque. The engine lugs, and the transmission starts slipping/shuddering/shaking trying to stay engaged under the tremendous load from the engine. I've also seen them try to go into 2 gears at the same time causing similar results. I really think you need to get it to a transmission shop unless you're pretty snappy with automatic trannys.