Does the squat make thigh swell?

Yes but in good way: When squatting and using the thigh muscles, what makes the thigh swell or get larger during the exercise is when water and blood and nutrients enter into the muscle being used. When people say they look 'pumped up' that is the above fluids that have entered the muscle. Doing squats is the best exercise for building 'the core' muscles or those that truly effect the rate of metabolism.