All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
First of all, we draw your attention that it is not permissible to reveal the private parts except in case of a necessity or a dire need. As regards a check up just to find out whether a woman is not sick, then that is not permissible. But if there are some symptoms that suggest that one is sick, then it is permissible to reveal the private parts taking in consideration that necessity is valued according to its proper value.
As regards the ruling of fasting, it is valid, but if you make up that day as a precaution then that is more appropriate, as some jurists stated that the fasting of a woman becomes void if something enters her private parts. However, if the check up does not involve entering something in the woman's private parts, then the fasting is valid without any difference of opinion.
Finally, you do not have to perform Ghusl (ritual bath), because making Ghusl is incumbent upon sperm discharge with desire. It is enough in your case to just wash and perform ablution.
Allaah Knows best.