I lean with no, ignore the guy above you. Subjectively an amp can make it sound a bit different but no amp will objectively 'improve' the sound quality.

The Dt770 (80 ohms) can be powered off of the 3.5mm jack on my 4 year old mid-range phone, I highly doubt your desktop can't power it properly.

There are two possibilities for what is going on:

1. Your not use to the sound, for some people it can take a month before they get use to a headphone. (I don't think this is the case)

Or

2. Everyone's ears are different, which I mean literally. Your ear shape could be causing the headphones to sound horrible for you. That's ok, I'm sorry that you had to find this out the hard way - however now people should be able to recommend better headphones to try.

Since you can't trade your headphones back, you may want to sell them on r/AVExchange - you probably will loose a smidge of money (shipping) however you can get really good deals for other headphones there, so it should even out in the end. Since the Dt770's were too harsh for your ears I'd recommend the Rode NTH-100, Sony MDR-7506, or Sennheiser HD 280 Pro. None have the piercing treble and all are highly recommended around this price point. That said, it would help to get other people's opinions on this. To my ears the Dt 770's sound great but I tend to like bright headphones.