Yes, it is normal to have puffy eyes after crying due to an adrenalin rush, which always occur in case of happiness, sadness, touching, or fear. It leads to twitch of your face muscles, constriction of your throat and redness and swelling of your eyes. What is more, you can try to apply a wash cloth filling with ice water to your eyes. Besides, cotton balls saturated with the milk can immensely help and bright your skin around the eyes. Further, what I used to eliminate the puffy and swelling eyes is to put slices of a potato or cucumber from vegetable crisper drawer. Well, it actually works. By the way, my sister says that the use of a ice-cold tea bags is great. Well, you can just have a try. Along with the methods above, you can also massage your eyes gently.