The two issues don't have to be related at all. It is entirely possible that they are in fact, separate issues. Pull the thermostat and drop it in some boiling water to see if it opens. If it doesn't, then you know what's wrong there and can move forward. You can also replace the oil pressure sending unit yourself for next to nothing.
do not do this unless u know ur theromostats opening temp. and u have a meat thermomator on hand.. and watch the thermo when it hits the desired temp it should pop open .. if it doesnt open at the right temp it will cause a over heating problem no matter what .. if u place in into boiling water of coarse it goin to open no matter what but u want..
ur thermostat could be a 165-195 degree thermostat depending on if has been changed b4.. most shops dont care what degree it is just that it fits .
so ethylene glycol in a 50% mixture with water can change the freezing point from 32 degrees Fahrenheit or 0 Celsius, to –35 degrees Fahrenheit or – 37 Celsius. It moves the boiling point from 212 degrees Fahrenheit or 100 degrees Celsius to 223 degrees Fahrenheit or 106 degrees Celsius. Pressure is the second way that the boiling point is raised; most vehicles have between 13-15 psi (pounds per square inch) in the cooling system. This can raise the boiling point of the fluid mixture approximately 45 degrees Fahrenheit or just over 7 degrees Celsius.
your problem could be alot of diff issues .. such as head gasket, radiator cap,waterpump, or thermostat .. even a cracked block, and or head.. anything that can upset the pressure created by the water pump . or no pressure at all ..
i would do a pressure test on the radiator .. or (if u have on hand) a lazer temp gun .. and run the car and point the temp gun at the thermostat and the hoses and see where its starting to get hot at . (this is without having to take the theromostat out .
... or u can always fill the radiator ... run the car .. open the radiator cap watch the fluid .. when the thermostat opens the fluid should drop or start to swirl ..and at all times someone watching the temp . if the water starts to swirl or drop and suck then the thermostat is fine ..
and just another thing i learned..."never let ur girlfriend take the car for a oil change" lol