Hi AnalogJ,
Pillows can certainly affect pressure and alignment issues and can be a very useful way to alleviate some type of “symptoms” on a mattress. A pillow that is too thin and isn’t supporting the head and neck in good alignment can certainly contribute to shoulder pressure and it’s not unusual at all for someone that buys a new mattress that is different from what they were sleeping on before to need a new pillow with a different profile. There is more about this in post #2 here along with some other information that may be helpful and post #45 here and post #10 here also include some discussions about pillows and pillow placement that may be worth reading as well.
Phoenix