We had very similar issues around 3 months. I think my little guy was going through a growth spurt and started teething early...got first teeth at 4 months. This book helped us a lot.
http://www.amazon.com/Healthy-Sleep-Habits-Happy-Child/dp...
You have to pick what is helpful in the book. Some people want babies to cry it out that young, but I always felt like my baby still wanted to eat, and I just did not agree with "forcing" him on an adult sleep schedule.
I totally believe in swaddling and someone gave us the BEST swaddle blanket:
http://www.miracleblanket.com/index.htm
It seemed to work very well. Our baby could get out of other swaddles in no time, but he did not learn to escape this one until he was about 4-5 months.
Your baby might need to go to sleep earlier. I know that sounds crazy, but we do bath at around 6, and then jammies, book, and nurse while swaddled. That puts him to sleep and he would stay to sleep for awhile. When he woke up at that age, I would change him, re-swaddle, and nurse back to sleep. He did not learn to fall asleep on his own until about 4-5 months...so at that point he had to be nursed/rocked to sleep.
We also used a noise machine with a soothing calm noise that helped him from waking up to any noises in the house.
Every baby is different, and I am just sharing what we did. I know how hard it is to be waking up so many times at night. I also took that 9-11 nap with my guy, and it always helped me after a tough night. Sometimes, when I just couldn't do another wake up at night, I would bring him into bed with me and nurse him on my side and let us both sleep for a couple of hours.
Hope something in here helps, if not just the fact that you are not alone in this and it is a normal thing...just a very hard for everyone involved!
Best of luck and let me know if you want to chat about any of this.
N.