Is it obligatory to change underwear after feeling urine drops exiting, then a single drop comes out after checking, and is taking precautions in this case considered doubt?

You are not required to change your clothes or wash them. The default assumption is that they are pure (tahir), and they do not become impure (najis) merely by doubting that they have been affected by impurity. Furthermore, changing them because they might be impure could be a gateway to obsessive doubts (waswasa) and opening the door to uncertainties.