Hi H.,
My youngest is about your son's age and she is going through a very clingy phase right now. Something I have been doing that seems to be helping is, I ask her if she wants to help me do whatever I'm doing. When I cook dinner, I bring in her little step stool so she can "help" me do the cooking - maybe let her pour ingredients in or stir a bowl of something, whatever she can manage (or I will give her an empty bowl and a whisk, that seems to work just as well). It keeps her happy, I can keep an eye on her, and she gets to spend time with me. She also helps me sort the laundry into lights and darks, and helps with folding the socks and underwear, then carrying the folded laundry to the appropriate bedrooms. And she loves "washing the dishes" (sometimes I will even put clean spoons or tupperware into the sink so she can wash them). I feel like it is teaching her some useful skills for later, and she feels very important that she is my "special helper." Maybe this will work with your son too. Granted, with a child this young, having them help really makes the task that much harder for mommy, but if it keeps your toddler from crying, the extra effort may be worth it!
Good luck to you!