I'm so glad to see you've already gotten some good advice here. Which surprises me since I've found many of the moms who frequent this site to be, how do I say this, a little too "tough-loving."
It's true, you CAN NOT spoil babies, especially a 4 month old baby. But we live in a messed up society that encourages us to hold baby, but not too often. Nurse her, but not when she demands. Help her sleep, but according to our sleep schedule, etc. It's like we force independence on our small children before they are naturally and instinctively ready. So go ahead, hold and love on that baby as much as you want. Besides, you spoil children with PRESENTS, not PRESENCE!
Check out this article from Dr. Sears on "spoiling":
http://www.askdrsears.com/html/10/T100200.asp
Here's an excerpt: "Few parents make it through their offspring's babyhood without being told that all their efforts to nurture and respond to their baby will surely spoil her. And if it's not spoiling that they're warned against, they're told not to let themselves be "manipulated" by baby."
Sound familiar?
Here's a link to kellymom.com. Especially check out the bottom of the page where there is a section of yet more links to great articles on this subject. You'll find out real quick that this is normal baby behavior AND there is scientific data to back up why you SHOULD respond to baby with the cuddling and holding she wants. No need to "train" or "teach" her anything.
http://www.kellymom.com/babyconcerns/fussybaby.html
Here's an excerpt: "Studies have shown that when babies are held often and responded to quickly, the babies cry less, and the parents learn to read baby's cues more quickly. A young child's need for his mother is very intense - as intense as his need for food. Know that your child really needs you. It is not about manipulation or something you can "fix" with the right discipline. Often a baby who is perceived as fussy is simply a baby who needs more contact with mom (and is smart enough to express this need) and is content once his needs are met. See the links below to read more about"
It's natural and normal for baby to want mommy only at this age. But it's also normal for mommy to feel overwhelmed. Don't feel guilty about wanting a break. Just keep trying what you've already been doing by letting her stay with others for small amounts of time. As she gets older, this will get easier for you both. My baby was the same way. I never forced us being separated on him and I NEVER let him cry it out. Now at 25 months, he's perfectly independent and stays at the sitters, at church, at my parents perfectly fine.
Good luck and best wishes to you!!