I recently purchased a 2003 Discovery 2 (which I love btw). When I accelerate its making a squeaking noise and when I let off the gas it quits. Sounds like it’s coming from underneath. Could this be attributed to one of my U joints? Can anyone help? Thank you!

 

Yes, this is a tell tale sign that the U-Joint is going to fail soon. At first its a squeak. Then it sounds like birds chirping. Then it breaks. Replace it asap.

 

You're lucky that it's giving you this warning sign. Many times there's no notice at all before the front driveshaft detonates and takes out the transmission or the lower case of the engine.
As mentioned, replace the driveshaft immediately. I would not drive it until you do.