Help. My five-month-old needs to be held day and night.

I have a five-month-old son. He is my third child. I am having two problems, 
both connected I think. For the last five weeks or so he has wanted to be 
held pretty much all day. Needless to say, I can't do that and at times he 
just cries and cries. When I nurse him, he falls asleep but only takes quick 
catnaps because when he wakes up, he can't get himself back to sleep. 
This can go on all day; I can get nothing done. I am lucky if I can get 
my other two children lunch. 
     I am exhausted and resentful by the end of the day and too tired to 
do the things I need do. I have some outside help for a few hours a week, 
and my husband is supportive, but I need to break my son of this habit. 
I am a firm believer in not letting babies cry - my other two children are 
very secure and confident, so I know letting him cry is not the right thing. 
The night is not much better. If he wakes up he needs to be held to go to 
sleep. Some nights he sleeps ten hours, and some nights he is up after five. 

A.B.R., Evanston