I have a 93 F150 4x4 regular cab longbed. I don't have a carrier bearing (seems important for this issue?).

Whenever I takeoff from a stop, I feel some sort of delay...almost sounds/feels like something is sliding back in the bed. I don't have a spare underneath the truck either. Is there something wrong with my differential?

 

I would take a look at your rear leaf springs. You may have broken or loosened your U bolts or spring pack bolt. Also look at the rear shakle hangers. They may have rusted.

 

It could possibly be some teeth missing on either the ring gear or pinion gear. From what I remember when I stripped the teeth off my pinion gear a few times, that's what it felt like.