In my third trimester with each pregnancy I always get burning on the Surface of my skin on the right side of my rib cage just to the right of my zyphoid process. My midwife said as long as it's not coming from under my rib cage where my liver is than it's ok. Because I get this with each pregnancy and my blood pressure is fine, I'm not worried.
My doctor told me if I'm having stabbing-type pain up by my ribs, it is an indication of preeclampsia. You may want to call and check?
I'm 38 weeks and I get the same pain, no idea what it is! I never think to ask the doctor at my checkups though.