Normally, when I'm just playing at lessons or at home, my tone sounds fine. However, when I have to play in stressful situations, let's say right before an audition or a performance, is there a reason my tone sounds a little "fuzzy"? And by "fuzzy" I don't mean noticeably airy/unclear to the audience (b/c apparently the judges never notice), it just doesn't resonate as much as I'm used to. When I hear this difference, I feel sort of uncomfortable. Could it be the acoustics? Not sure about that, the chances are slim. Could it be that I'm tensing up because I'm nervous? Or could it all be psychological? Not sure, but this situation happens to be all the time when I'm nervous. What can I do to fix this?

Ah the evil fuzz!!!1
If the audience isn't hearing it, don't worry about it too much. Several things could be happening.
1- if you are nervous and your senses are pumped up you could be hearing something that is barely there all the time, just more noticable when your senses are on edge.

2-When we are nervous sometimes the moisture level in our mouth changes. Either way wetter or drier can result in the embouchre acting a little differently. So there could be a little buzz/fuzz there.

3- I have lots of good friends but I don't trust their opinions of my playing. Only three people do I really trust to tell me the truth and be good enough to hear what I want them to hear. Do some tests on some of your friends to see how honest they are with you in music.

Another thing you can do is record yourself. Next audition or public performance have a recorder near you (in your case, your jacket pocket) and then listen to the tape to see if you can hear it in the tape. There are a lot of sounds that don't make it more than a foot or two away from you when you play. So the audience never hears them.

Just keep playing in front of people as much as you can.

I used to get so nervous I would sound like a goat bleating.

I have gotten better.

Try to find more chances to play for an audience.

many times, depending on the accoustics, you will hear more edge or airy sound up close, as the sound travels it changes, if you can get a good recording of you playing when this happens it will help..just don't force, nerves can cause that to happen

Thanks for the advice guys. I'll work on that.