Sounds like normal nursing adjustment period to me with the information you gave. Babies know how and when to increase supply and it sounds like this is what she may be doing. 10-20 minutes of vigorous nursing every 1 hour will build milk supply faster and more effectively than nursing every 2 hours. These are referred to as "frequency days" and often will go on for 3-5 days and then slow up back to every 1 1/2-2 hours. The spurts may often occur at major growth spurt times around 3 weeks, 6 weeks, and 3 months ("The Womanly Art of Breastfeeding"). You may notice these later when teething or major development burst happen as well. This is your baby demanding what she needs and your body reacting to her. This is why on demand nursing is important, especially in the beginning.
The only thing to watch for would be that she is getting to the rich hind-milk at each feeding (let down and for about 5-10 minutes after is usually fore milk, hind milk comes after and is richer in calories and fat). Sleepy babies who don't finish need help early on. Switch nursing can help. When you notice her sucking go from vigorous as with the let down, then to more flutter sucking when she is starting to doze, take her off and burp her or change a diaper. Then offer the other breast...when she starts to dose, than take her off and burp her and put her back on the other again. This can ensure she makes it through the nursing, and she is getting the hind milk from at least one breast every feed. As she gets more hind milk she will start sleeping less at the breast and be a more active nurser. Eventually as your supply is established and she gets more hind milk, you can even go to offering just one breast at each feed.
Nightime nursing is also important at this time for weight gain and milk supply. If you aren't opposed to it, like Rebekka said co-sleeping can really help out here until you get into a groove (most by 6-8 weeks). Getting adept at nursing lying down will help you gently wake, feed and drift back to sleep later on (barring she doesn't need enzymes than we still have to wake a bit more than most moms, but sounds like she doesn't need them yet).
In the early, sleepy weeks, I placed a pillow above and next to where he laid (on the outside edge) and kept my boppy close by since I could never nurse laying down until later (boobs to hard at first). When he'd wake, I'd unwrap him, change his diaper, and leave him uncovered for the most part. We'd nurse sitting up in bed and often I'd drift back to sleep with him on my chest (after a quick burp), blanket tucked underneath me like a little envelope, and my arm propted up on the boppy. Sometimes I'd place him next to me and sleep with my arm around him. They don't move at this age and if they do it is just to find you...very safe. Most babies don't sleep through the night until much, much later. If they do it is the minority and you are one lucky momma.
38 weeks is considered full term and if you aren't having any nipple soreness or breast tenderness, more than likely her latch is good (looking for a wide open mouth around ariola with clear sucking and swallowing sounds). Most pediatricians don't have tons of breastfeeding knowledge...you may get the most help from a LLL in your area or a lactation consultant...but to me it sounds like normal stuff. Hang in there.
That said...it is exhausting beyond belief but as time goes by the benefits will reward you for your brown bags and blood shot eyes you have now. Great ideas on the basket of goodies for your toddler.
Unless you really need to for some reason...I wouldn't worry about pumping until this passes in a few weeks. Are you needing to pump for storage to return to work? As things even out I could find out some info on pumping strategy that won't drive you crazy;-)
You can do this...think of all the other tired nursing moms up at the same time as you ;-)
Warmly,
Jody
