Hi, J..
It sounds to me that, in general, your daughter is overtired. At 10 weeks old, she should be having 3 or 4 decent naps during the day to break up her periods of awake time, and she should be sleeping a solid 12 hours at night (although mine's never done more than 10, 11 when she was sick) with only one (or sometimes 2) wakings to eat. Does that sound like Heaven? It can be done!
I highly recommend reading (READING? I don't have time to read! Believe me - you DO, and you'll thank yourself when you do it) The Baby Whisperer: How to Calm, Connect and Communicate with your Baby. It is available at my local library, and that's where I read it. My daughter was a miserable cat-nap only and 5 hours ONLY overnight sleeping baby ... and by 8 weeks, I was exhausted and ready to try anything (including crying it out). Of course, we had MORE issues than JUST the short sleeping, and THIS book really helped me out.
Babies thrive on patterns, routine and consistency. It takes time to help to establish, but it can be done! My DD now still only sleeps about 10 hours a night but has 2 completely predictable daytime naps (short one in the morning, longer in the afternoon) and starts falling asleep at roughly the same time every night (on the dot). Morning wake up is inconsistent but generally falls closer to 7 am!
It's hard with a newborn. It really is. But what is key when they're so young is teaching them to "self-soothe" so that they can fall asleep on their own with minimal intervention from you because they WILL wake multiple times in the night (we ALL do, but as adults we're accustomed to sleep and have no need for mom/dad to fall asleep again) and unless they're truly in need of something (potty, diaper change, food, pain relief), they can allow themselves to fall back asleep again. (My daughter, now 13 months old, took really well to having more of a structured day/night and reliable routines ... and she's much more pleasant for it as well.)
Good luck to you!