It is very common for a two-month-old to have gas and mild spitting up. Sometimes, babies stiffen or arch their backs when trying to pass gas. However, because your baby is so young, it is not safe to give any medications without a doctor's guidance. Please consult your pediatrician to evaluate the body stiffness and ensure it is just normal straining. If appropriate, the doctor can recommend safe options like simethicone drops, with a dosage precisely tailored to your baby's weight. For now, try keeping your baby upright for 20 minutes after feedings and gently massaging their tummy in a clockwise motion.