hi i have a 1986 Buick LeSabre Custom and you can rock the pulley
back and forth on the water pump and it overheating wood it make
it overheating i don see no leaks

Sounds like you need a water pump. Also check your thermostat and cooling fans for proper operation.

The rocking pulley denotes a bad worn bearing. If you listen close you should hear a whine sound. Very easy to replace, have done many on this line. I own a '90, girlfriend had a '87, friends had '88 and '89 and did pumps on all of them. Just drain your radiator, remove serpentine belt(sometimes easier to remove windshield washer resivoir and anti-freeze overflow tank first) several bolts and your home free. Also remove the pully bolts first with belt still on. Where I live there is only $10 difference between rebuilt and new. About $30 for new Bosch pump-Go new! Good Luck!