However, I'd bet this is what might be happening. You learn a chord, like Emaj, then Amin, then say a B7... each chord you can play no problem, but that B7 WAS a little bit tricky to get right... strum... sounds clean, good to go. Now you start playing the chords together, making music and *bzzzinggg* you start hearing buzzing strings.
What to do:
-for any given song, play all the chords you'll need to know one at time, strumming slowly once so you hear each string, and make sure it plays cleanly.
-once you have that down, start playing the chord progression, slowly, making sure you have the changes down pat, and you don't have bad notes.
-if you get a buzz or dead sounding note, FREEZE. Look at your fingers and see where the problem is. Buzzing is usually caused by a fretting finger's fingernail (say that 3x fast!) rubbing up against a lower string. A plinking or muted sound is ofter caused by the fretting finger touching the string above, or not fretting the note hard enough to get a clean tone.
When you freeze and see the problem, correct it, make sure you can play the chord cleanly. Then, go back to the chord before, play through slowly to where you had the problem, and continue, watching your fingers. Chances are, you're adjusting your hand position as you change chords, and moving your fingers into a position that causes a buzz. Happens to me all the time with new chords, or chord progressions, especially with unique fingering patterns where I'm changing notes within the chord as I play.
The good news is that it doesn't take long to correct. Just freeze when you hear the problem, visually confirm where the problem is happening, correct it, and then play through that part again, going as slow as you have to in order to play through with no mistakes or buzzing strings. In no time you'll be playing cleanly, but make sure you don't try and "work it on the fly". If you just keep trying to play through and hope that the buzzing will get better on its own, chances are it won't. You have to work at it, but it doesn't take much.
Also, make sure your fingernails are trimmed nice and short on your fretting hand, as this will allow you to really get the pad of your finger vertical and minimize chances of buzzing.
Good luck guys!