I would also add to have your doctor check to see if you have scoliosis ( curve of the spine ) I have that and I also get back/side spasms from this.
They could both be unrelated - nausea after eating could be a number of things, pregnancy, overeating... the list is endless. I get spasms in my back, which are muscular spasms. MY_Khan could be right about it being your posture. But please go to the doctors if you are worried. It's impossible to say what it could be without being checked out first. Good luck.
This may be due to your sitting posture if you are a working women, or can be due to indigestions, if you don't have good movements after your food.
Watch yourself and you will find the answers.