When I had thrush, it really felt like fire and was incredibly painful until the milk let down and then the pain decreased from excruciating to bearable. However, by the time that my doctors finally prescribed me anything, I had a systemic infection that required 20 days of Diflucan to cure. So if your doctor suspects yeast I would definitely treat now before things get really bad. Yes, you'll want to have your little one on something at the same time. Does your LO have any white patches in the mouth (not the tongue)?
We were fine on the thrush medications with no side effects.