I'm wondering, could a sitting U.S. Senator run against the other sitting U.S. Senator in that state?
The only requirements are those specified in the Constitution, regarding age, citizenship and residence. Title 2 of the US Code has laws regarding elections governing timing of elections and soon, but nothing like a law saying "No sitting US Senator can run for the other senatorial position in his state". This article reviews aspects of congressional qualifications, and it is noted that the courts find that the constitutional qualifications are exclusive, meaning that there can't be such additional requirements. Therefore, convicted felons can be US Senators.