It does sound like you have a problem. More like a concern, actually. A good
synthetic oil will handle those temps just fine, but the temps are kinda high. it also sounds like your gauge is fairly accurate. Not perfect, but few of them are.
Another question is, does the cooler work? Maybe your thermostat isn not opening. But even not working/connected, temps should be lower.
What's the pressure? That's another thing that will increase the temp.