She's cluster feeding. They do that to fill themselves up so they can sleep for a longer stretch. It's also related to growth spurts, and sometimes to colic as well. Although babies who aren't colicky will cluster feed as well.
Although you may feel "dried up", you aren't. Your baby's nursing stimulates milk production. So, as long as baby is suckling, you are producing.
Are you going to mess with your milk production? Yes. Any time you supplement you reduce the amount you produce. Milk production is supply and demand. The more baby demands the more you produce. Supplementation is a slippery slope. If you are honestly not producing enough (you'll know this by a lack of wet and poopy diapers and by baby not gaining weight) then supplementing is a good option.
However, sine what you describe is normal, and she's gaining weight, you don't have a reason to supplement. If you nipples are getting sore, you can use a Lanolin cream on them. Also, if you let them air dry in between feedings they'll fair better.
One of the best online resources for breastfeeding is http://www.kellymom.com/ go check her out for more info. Or you can contact me http://www.shininglightprenatal.com I'm a Lamaze instructor, and I teach breastfeeding classes too.