Question: I get this really bad feedback sounding noise when I play stuff like this, from the beginning of the Free Bird solo, 
shown in tab:

```
1  ----18---18---18---------
2  -18---18---18---------

```

(All notes on second string played with a full bend.)

It's there on any amount of distortion, but not when I play clean. Is it a problem with the amp? If so, what can I do about it?

Answer: 
Is the amp solid state, digital, or tube? Is the volume high or low, does reduce in gain and/or decrease with volume? Can you reproduce the sound without bending(could be an artifact bends not in tune). Is your guitar intonated properly?

Note that the guitar uses equal temperament and not all notes are in tube. m3rd's with a lot of distortion of a specific type can sound pretty bad. With class B tube amps you must turn them up because they have intermodulation distortion which is almost at a constant volume but can be masked with volume. That is, the louder the amp the less you will hear this type of distortion which is very annoying. Solid State can suffer from this too but digital won't.

Distortion adds harshness to a sound and it can be emphasized with certain notes and intervals. Distortion can come from a wide variety of places in an amp. Some good and some bad. Sometimes the "bad" distortion can be good in some context.

Naming the amp you have, if you can reproduce this sound on the clean channel with slight over drive, and a clip of the sound will help(although I think I know exactly what you are getting at as I have a similar issue with my amp ATM and I'm in the process of tweaking it to get a smoother distortion).
Before "throwing out" your Amplifier I would suggest trying a different guitar! A good guitar with good mics will sound at least resonable through a bad amp, while a bad guitar will sound crappy even through the best amps. I looked at some reviews of your guitar since I am not familiar with that model and it seems like feedback noise is something that many people get with it... A more expensive amp will probably not fix your feedback issues either since the problem lies in the wiring of the mics.
Hope this helps!

"It can't really handle being cranked through an amp too loud because it feeds back and isn't made for anything huge"
<http://www.ultimate-guitar.com/reviews/electric_guitars/first_act/me300/index.html>