Will the wrong size radiator cap on the radiator cause it to overheat

Th cap can be a problem it can easily be pressure checked, but normaly you should have hte whole system pressure checked to see if you have an internal leak. Also disconnect fans if electric with engien off when it's hot place h and in different spots on radiator fins. If you feel a cool spot then ti's probably bad as it should be teh same temp all over.

Have you had the radiator checked for internal blockage, a back flush will not show up any blocked core tubes, the radiator must be removed and tanks taken off and tubes cleared of any sediment.

The cap at.9 atm is slightly under pressure but this will not be the primary cause of such rapid over heating, you should have a 1.1 rated cap, possibly a faulty thermostat causing no circulation, water pump impeller corroded away, coolant leaks causing air locks, ensure that these are all not an issue in your case.