Hi, is swelling under your eyebrows common after microblading?

This is totally normal so don't worry.  When ever there is trauma to the skin there will be some swelling.  In this area, when you are upright, the swelling will settle below the brow because of gravity.
It will go away soon--if not in a few days, at most a week.  You can apply ice, do lymphatic massage and sleep with a neck roll so your neck is slightly extended.  This will allow some of the fluid to disperse to the forehead and make it less obvious while it is absorbing.  The pigment will change color somewhat during this process so do not be alarmed.  Wait a good 4 weeks before making any judgements on whether you like it or not.  
I hope this is useful info.  Best of luck to you,
Dr. Amy