A strong coughing fit can strain the muscles of your abdominal wall and rib cage. At 16 weeks your growing uterus has already stretched those same muscles, so they strain more easily. The tightness and pulling you feel on both sides, worse on standing or after eating, with no lower or back pain, fits this muscular pattern rather than a pregnancy complication.
Next Steps
Rest the area and avoid heavy lifting or sudden twisting. Eating smaller, more frequent meals can ease the pressure that triggers it. Treating the cough itself with steam inhalation and warm fluids will help it settle faster.
Health Tips
See your obstetrician if the pain turns sharp or one-sided, you notice bleeding or fever, or breathing becomes difficult.