Does a small amount of urine from my baby girl, getting on my hand while changing her diaper, make my clothes impure, and is the impurity transferred to me when I carry her if I don't wash my hand after that wetness?

You must take precautions to prevent the impurity of your infant's urine from affecting your clothes, body, and place, and purify what is not difficult to purify. If you strive and some of her urine's wetness afflicts you, which is difficult to completely purify, then you are not required to purify it, because it is something difficult to guard against. Therefore, her clothes are not deemed impure, and if you carry her, the impurity will not transfer to you. Some scholars have stated that a nursing mother and those in a similar situation for whom it is difficult to guard against impurity are required to strive to ward off the child's urine. If something afflicts her after her striving, then washing it is excused due to the difficulty of avoiding it. Some of them recommended washing it if it becomes excessive, but it is not obligatory.