What would cause a dull ache and pressure in the area that stretches above the public bone, along with tenderness when pressed?

A few things: Your bladder lies deep to that area, but there's also skin, muscle and connective tissue in-between, inflammation of any of which could cause what you're describing. Pain with urination or a sense of urinary urgency would suggest a UTI (bladder infection) which is something that can often be treated via virtual consult or sometimes with an after-hours phonecall to your primary care doc.