If possible, keep breastfeeding your baby. Breastmilk is less painful for them to bring up than formula. My daughter is in the same boat, and her pediatrician prescribed Zantac to make her stomach contents less acidic. Your baby will probably continue to spit up, because it seems to be a physical condition (the valve at the top of the stomach isn't strong enough yet). I suggest more frequent burping, keeping her more upright after feedings, and lots of love and patience!
Mylicon drops help with gas, and my pediatrician recommends giving them regularly (every 4-6 hours), even if the baby isn't fussy. That will help keep the baby comfortable.
As far as constipation is concerned, your baby probably doesn't have a problem with it. Breastfed babies usually don't poop very often after the first couple of weeks, since their bodies are making such good use of the milk (very little is wasted). One of my sons would have only one bowel movement per week, and yes, it was always a huge mess when he had it!
I can definitely relate to your frustration. I hope your baby feels better soon!
Mom of nine, ages 22 to 2, six boys, three girls.