I have recently gotten a new, stronger prescription for contacts. Could this be making my eyes fatigued?

Absolutely. If you are given too strong of a prescription, your eyes are forced to focus harder in order to adjust for it. This can lead to strain and fatigue. If the distance vision is good but the strain is occurring when trying to read, you may be starting to need a near vision prescription, or possible over-the-counter reading glasses. See your eye doctor and have them check your prescription.
Yes. If your prescription is set for far distance tasks and you do a lot of near work, your focusing muscles will have to work harder. If symptoms do not improve in 2 weeks you should reconsult with your doctor.