Oh dear, I can sympathize. My 4 month old has gone through the same stuff. In fact, I have recently realized that these frequent feedings and refusal to nap is more than just a growth spurt. She has been becoming increasingly sleep deprived and overtired. If you haven't done so already, go buy the book "Healthy Sleep Habits; Happy Child" by Marc Weissbluth. I was wary at first, but today is day 3 of our "sleep training" and my God I'm glad I took the chance. I've never been an advocate of letting babies "cry it out" but I'm learning that sleep, like just about everything else in human babies, needs to be taught.
I spent weeks wondering why my little one didn't seem to need much sleep until she finally started to break down and become extremely fussy and agitated. She'd been very easy tempered so the change was alarming. I chalked it all up to growth spurt or teething, but as I read descriptions of over tired children, it was like they were describing my daughter!
Our first night was hard, in fact it was the hardest thing I've done thus far as a new parent, aside from immunizations (which if you haven't endured yet, be glad, it was a heartbreaker for me). We put her down to sleep at 5:30 pm (quite a change from her normal 9-10pm bedtime). She cried for almost an hour then fell blissfully asleep until midnight when she woke up to eat. She then promptly fell back asleep until I woke her up at 7:30 am (wow!!!). Night 2 she also went to sleep at 5:30, cried for about half an hour and slept until 3am, ate then slept again until 7:30am. We are still trying to figure out her best nap schedule, she usually doesn't sleep more than 45 minutes at a time, but today she slept soundly from 12-2:30 pm! (The morning and afternoon naps didn't go quite as well, but progress is progress.) Tonight we laid her down at 5pm, she fell right asleep (NO crying!!!) and has been sleeping soundly since.
I must warn you, if you've been getting up alot at night for feedings, etc, your sleep might get worse before it gets better. We moved our daughter into her own room when we began all this on Sunday and between her no longer being visible in her cradle in our bedroom and having her sleep for such extended periods without awakening, I've been up quite a bit wondering if she's ok and checking in on her. Relax, she's been fine and one of these days, my sleep will return also! (At least I'm hopeful...)
I know, it sounds too good to be true, I thought so too. But it's actually working and the progress is encouraging, to say the least. Our happy easy tempered baby is back and I cannot express how grateful we are for that.
It sounds like you might be getting into an over tired pattern with your little one. It seems like they should know when to sleep, but again, they won't know until we teach them. The whole point of the book is sleep begets sleep and lack of sleep begets lack of sleep. It's true! I'm sure you've had times you were so tired you couldn't fall asleep...
Anyway, I'm blathering on because our success thus far has been incredible and if I can help anyone else avoid the weeks of turmoil, tears, exhaustion and stress we endured, then I'll be happy. Please don't chalk it up to a growth spurt, get the book!!! I'm pretty sure you'll all be grateful for it. (I know this all must seem like a shameless plug, but it has helped beyond my wildest expectations, and it's only been 3 days. Please give it a try;)