Lady Tut -
Many people have had that problem. Some guitars are wider at the neck then others. If your fingers are truly very large at the tip, then a wide necked guitar could be your answer.
That said, I think much more likely is that you need to develop the habit of using the tips of your fingers to press down on the strings just behind the frets. You want to press the frets down with the very tippy tips of your fingers and not with the pads of your fingers. If you use the pads or sides of your fingers, no matter how fine your fingers are, you will still mute the string next to it. Sometimes that is desireable, but it is an advanced technique. For now, just starting out, what you want to do is get used to curling your finger and using the very tips. This is easier if, when you hold the neck of your guitar, you leave a space between the crook of your thumb and the back of the neck about large enough to fit a magic marker through. Your thumb should rest on back of the neck, and you should have a space between the crook of your hand and neck of the guitar, then curl your fingers around to fret the strings. Support the guitar with either a strap or resting on your leg. Your fretting hand does not provide the primary support for the guitar.
Now a word of encouragement...There are very few other situations in which you use the very tips of your fingers like this, so don't be surprised if it takes you a little while to develop the strength and dexterity to do it. You'll also experience soreness in the tips of your fingers. We all went through that stage, and you will too. You'll make it if you stick with it. The first time you get a nice cleanly ringing chord it will feel worth it. Keep up the good work of practicing. Don't worry about how long it takes. That's different for everyone. Just stick with practicing with good form at least fifteen minutes a day and you'll be amazed at the difference a week, and then a month, and then three months will make to what you can do.
- Zurf
Granted B chord amnesty by King of the Mutants (Long live the king).
If it comes from the heart and you add a few beers... it'll be awesome! - Mekidsmom
When in doubt ... hats. - B.G. Dude