You can combine them without any problem, but there's an important detail. Omeprazole reduces stomach acidity a lot, so some probiotics won't make it alive to your intestines if you take them together or too close. Best thing is to space them out a couple hours, like you take the omeprazole and wait two hours before the probiotics, or the other way around. That way you avoid the stomach environment messing with the good bugs.
What they don't mention is that chronic gastritis often comes from imbalances in your flora, so probiotics can actually do you good in the long run. But here's the thing: not all probiotics are the same. Look for strains that are acid-resistant (even if it's just a little) like Lactobacillus or Bifidobacterium, and better if they're from actual pharmacies than random health food stores. And heads up, after two months on omeprazole you'll have already lost a fair bit of your flora, so it's worth giving it a try.
All that said, ideally you'd tell the doctor who prescribed the omeprazole that you want to try probiotics. He can recommend a brand that works well with your specific treatment. It's not because there's a direct conflict, but because he'll know better than me what kind of probiotics are actually gonna work for your case.