There is a small piece of glass in my foot. Should I try to remove it myself or should I see a professional?

Foreign object. Depends, if you can see it or feel it near the surface it may be reasonable to attempt yourself. If unable to, recommend you see a professional as it is very difficult to find sometimes even with the advantages of radiographs, ultrasound and other guiding techniques.
You can try removing. If it is superficial, you can try removing it by tweezers after soaking your foot in epsom salts and warm water. You should seek a professional if you cannot get it out.
Call me. Old fashion, i prefer the doctor removes it. Less chance of infection.
Out of room . Pour betadine solution over the affected area.If you can see the edge and if you have a steady hand i would take some small tweezers first clean them with alcohol then if you can gently grasp the exposed end without causing the glass to further push in.Pull back gently not too break off a piece.Clean the site with peroxide and clean water preferably hibiclens pressure, dress, elevate, tetanus . Ran.