My 3.5 yr old just went through this. We took him to the dr. and they couldn't find anything wrong. Then I read about Pollakiuria. This is what it is: Mostly affects children between the age of 3-8 years, and causes frequent daytime urination, sometimes up to 10-30 times a day, usually with very small amounts of urine being produced at each time. Children with pollakiuria usually do not have other symptoms, and it is not known what causes it, although it may be linked to stress. No treatment is necessary and symptoms usually go away after about 3 months. It is also called Extraordinary Daytime Urinary Frequency Syndrome.
We never verified this with a dr but it fit exactly what was going on. I think his "stress" was getting used to having a new baby brother. My son's symptoms have subsided the past month. We learned not to make a big deal about it and not ask a lot of questions when he had to go so often and that seemed to help. But during this we were really worried, so I know what you're going through. I hope this helps. Good luck!