Sounds like air to me. These engines are very easy to trap air in the cooling system. See if you can borrow vacuum fill machine or beg a dealer buddy for a vacuum fill. I see this all the time when someone has a F*** dealer or something do a cooling system repair on one of these and then gets an overheating condition and fluctuating gauge.

If you have driven more than once it should have leveled off by now showing low level but it is possible the trapped air never came to the top.

Does it have a functional level sensor?

Does the low coolant message ever come on?

What type of fan controls do you have?

If they operate by temp, feel of the air coming off them when the gauge shows 240+ and see if the air is hot. If it is, it's likely that you are actually overheating and the gauge is correct. If the air off the fans is cool, there's lots of air in the system or the tstat is stuck.

Now the bad possibility. I'd go to AutoZone etc. and buy a block tester to ensure you haven't lifted a head or popped a head gasket.