Two hours is very unlikely to be enough time for this self-connection.
You would need to clear immigration to reclaim your bags, and then check them in with the next airline yourself.
You can be visa exempt if you arrive from Dubai or Qatar with a visa/entrance stamp from those countries. It's also possible to obtain a 21 day visa on arrival, but only if your connection time is more than six hours. Timatic, the database which airlines use to verify passenger travel documents, states in part:
Visa required, except for Nationals of USA with a visa or an
entrance stamp for Qatar if arriving directly from Qatar (visa
must specify that it is valid for travel to Oman and must be
valid for at least one month on arrival) , or:
Visa required, except for Passengers with a confirmed onward
ticket for a flight to a third country within 24 hours. They
must stay in the international transit area of the airport and
have documents required for the next destination.
Visa required, except for Nationals of USA with a normal
passport traveling on business in transit for more than 6
hours can obtain a visa on arrival for a maximum stay of 3
As international check-in closes an hour before departure, you have 50 minutes to clear immigration, claim your bags, clear customs, and check-in your bags for your next flight. And that's if your arriving flight is on time. If you're an Olympic sprinter and immigration is quiet, you could pull it off. But remember Murphy's Law. Your flight may be late, immigration could be a madhouse, and you might be randomly selected for a customs check.