If you have diverticulitis, then you can get an infection. I think it's generally caused by eating small seeds (think strawberries) and having those getting stuck in the little pockets and setting up an infection.
But I am mystified as to why that didn't show up on a colonoscopy (I think that's generally how they find it) and why you have an infection but no fever? I don't know that I've heard of that before. And he didn't even do a white count? Sounds shady to me, like guesswork. I can't tell you to not do something that your doctor told you to do, but depending on how much I trusted the doctor and how much sense he made to me when explaining why he thought I had what I had, I personally probably wouldn't take the antibiotic until I got a second opinion.
IBS flares up, comes and goes. You may just be having a worse time of it right now. I suddenly and without good reason developed daily diarrhea back in the summer that lasted about 2 months before I got medicine to straighten it out (Welchol for my lack of gall bladder, calcium for the excess water in my stools). Who knows what makes things like that come on?
I have read that the penicillin-related antibiotics are more prone to causing diarrhea while you take them and make you more likely to develop a bad bacteria build-up afterwards (antibiotic-associated colitis). Here's the Catch-22: if you have a bad bacteria build-up, the antibiotics will kill it off. But having wiped all of the bad stuff out, bad stuff may just come back in. And if you don't have a bacteria overgrowth problem, you may develop one. If you do decide to take the antibiotics, then make sure you take BILLIONS of probiotic cultures daily. We're talking two-three times the normal dosage of that stuff (I found a doctor's website online that said he made people take that much in order to keep them from developing diarrhea or C. difficile, etc.). And make sure you continue to take large amounts for a week or two after stopping. That should keep you from getting the bad bacteria in there. I think the best kind of probiotics to take are the ones that feature several different strains all together, not just acidophillus alone. My G.I.'s nurse swore by Culturelle. A lot of people here like Digestive Advantage.
Oh, and this is something your doctor should have talked about, but if he's not all together with it, he might not have. People who are allergic to penicillin are often allergic to ampicillin and/or amoxicillin since they are derivitives of it. If you are allergic to penicillin, I wouldn't take the ampicillin. I had a doctor put me on it once--telling me that only 1 in 10 people allergic to penicillin are allergic to ampicillin--and guess what? I was allergic to it. I think I had a much smaller reaction that had it been regular penicillin, but it did cause me to itch really bad on my face and ears (of all places). If you're not allergic to penicillin, then it should be okay but for the bacteria problems listed above. But having suffered an allergic reaction to it, I just wanted to make sure you knew about it in case you are allergic.