Hi Alaina,
Welcome to our group! I hope you will find us to be congenial and helpful.
As for your original question- no, you only need new undies.
On a more serious note, if you wear snug-to-tight jeans you will need to go up a size. That should give you enough room to be comfortable as well as still feeling attractive. Warning: the idea of wearing pullups or briefs with lots of SAP only works until it gets wet. Then they balloon up much more then those with little to no SAP.
If you wish to stay trim looking, you will need to keep several diapers on your person "just in case" as the thinner diapers don't last all day as you have found out. In time, you will grow to understand how long you can go between changes with your routine and the brand of diapers you use most. "On your person" may mean that you only keep one in your purse/briefcase/backpack/laptop case, but there are more in the car trunk for back up. We all do this as even the most dependable diapers do leak sometimes, and it's always at the most inopportune moment.
Another consideration is color- wet spots on dark colors don't show as much. I have black denim jeans for that reason.