Physical symptoms can I expect after facial laser cosmetic surgery? Looks like my face is sloughing off.

Depends... The expectations depend a lot on the type of laser and depth or treatment. Your doctor should have told you what to expect. For a deeper level of treatment, the degree of redness and swelling can be high. Contact your laser surgeon to answer your questions, and be sure to ask questions before the procedure if you aren't sure what to expect.
Which laser? After resurfacing with co2 and erbium-yag lasers, it is common to have some swelling, redness, and sloughing of surface. Be patient and follow your doctor's instructions on how to care for the surface and gently remove the separating skin cells. Stay in close contact with the provider to insure you are not experiencing unexpected skin reaction.
Old skin peeled off. It depends on type of laser. If it is an ablative laser like co2 laser (for example active fx), your skin will slough off or peel off. If is non ablative laser like fraxel, you will see minor sloughing off of your old skin or dryness.
Peeling is normal. How the face heals after laser treatment all depends on what kind of laser was used. Some lasers have minimal healing time but these also result in less improvement. Many lasers have 2-7 days of peeling and these in general result in more improvement of age and sun related skin damage. Be careful to avoid the sun while you are healing.
Laser Recovery. This can be a normal reaction. It is best to ask your doctor what to expect from the specific treatment you underwent.