Sauerkraut, kim chi, kefir - all with live cultures -- those are awesome foods for you! Another very, very helpful food for gut issues is bone broth. You simmer bones in a crockpot for a couple days, along with some apple cider vinegar -- the broth it makes is chockful of extremely good-for-you minerals, amino acids, and gelatin - good for overall health but specifically for healing intestinal lining. Try googling bone broth and the GAPS diet. (The GAPS diet in general might be helpful for you at this point.) Here's one link:
Re: specific probiotics, you'll want to do some research if your doctor can't provide you with high-quality ones (better than than you can just grab at the store). A lot of good ones are available online. It can feel like a bit much trying to figure out what's necessary - but if you google SIBO and probiotics, you will probably find some good recommendations. Best to ask your doctor for recommendations - but if s/he isn't aware of how vital they are, you really might want to find a second medical opinion, too.
There's a lot that's still not understood about gut flora and not all 'old-school' docs are aware of a lot of the research that's come out in the past couple years -- it's becoming increasingly clear that a healthy bacteria population is absolutely crucial to our overall health, not just stomach issues. If you want to do more background reading on the subject I'd recommend looking at Chris Kresser's website for starters. (This link might be up your alley at the moment! http://chriskresser.com/a-healthy-gu...to-weight-loss
Sorry for the novel, hope something's of use! Long story short is that there's so much you can do to help yourself heal with diet and probiotics! It's daunting at the outset to learn so much stuff, but also really empowering to actively help your recovery. Good luck.