Worth a phone call to your doctor; they get paid a fortune for a reason. They deserve to deal with phone calls from patients. ;) However here's my reaction:
Everything sounds pretty normal except the diarrhea which I would really think probably has nothing to do with the immunizations but would be some sickness he might've picked up at the doctor's office.
As for the sleeplessness, yes that's casebook normal after immunizations. Fussiness same thing. Spitting up is a result of fussiness because they're crying/screaming so their tummies are gettin a workout and that makes a baby spit up.
In general I'd say call your doctor but it's not worth worrying about. My son FLIPPED OUT after his first immunizations. Same thing you're describing but in place of the diarhea was a low fever (common, i found out, after immunizations at the beginning). I was worried, angry... why oh why did I get those stupid immunizations? I did find a few things that helped out later on (now that I'm a seasoned expert and he's 17 wopping months old haha)
1) After immunizations take baby home for a warm bath to relax his muscles.
2) Don't plan anything else for that day and possibly the next; no friends coming over or anything (or just one but not like... a bunch-- over-stimulating). The baby needs to chill out not get stressed.
3) The baby will be a little sore and is also trying to fight the medicine in the immunizations (which is the point so it's good-- they're doing their job), so the baby will be a little fussy and tired, and when babies feel like that they're clingy. So I've learned to prepare myself for that and expect the clinginess and co-sleep and carry him around all day on my chest after immunizations. Lots of comfort nursing. (I'm writing this in present tense but my son hasn't experienced the symptoms you're describing for many months-- it gets better-- the first one is the worst. Last time my son experienced no misery at all.)
4) Don't get excessive immunizations. Get the necessary ones and wait for anything else till he's older. They start needing fewer immunizations after the first year so that's a good time to get the extra ones. My dr. wanted my son to get the chicken pox vaccine and the flu shot this year and I was like "Oh come on. You're already pumpin the kid full of medicine and now you want him to get 2 more shots that didn't even exist when I was a kid and I'm fine? Can't I wait a year? He's not even in daycare or anything!" and she said that was fine. That first year is brutal-- their tiny bodies are getting so many immunizations. I personally don't like the idea of adding more to them. What's a year? Get the "extras" the next year when they don't have as much to deal with.
Anyway, congrats on your kid, welcome to the world of motherhood and never knowing if you're "doing it right" and your kid is "normal." Did you realize when you gave birth that you were signing up for a lifetime of worry? lol well it's worth it, good times, good times. He'll be fine in another day or so. Just cuddle him and soothe him!