Should i be experiencing back pain if i am 3 weeks pregnant?

Not usually: This is not a usual pain in pregnancy. It is probably due to some other cause. Lower back pain is usually what we call "musculo-skeletal" pain - meaning arising in your lower spine and pelvic bones and their surrounding muscles. This is best treated with rest, back exercises (find them thru google on the internet) and a heating pad. If the pain is very severe it is best to be checked by your md.