Is it normal to have under eye bags after laser round the eye area?

If your laser procedure was performed recently, as the other doctors have explained, the procedure itself can cause temporary swelling. This should resolve within one month. some people are more prone to swelling in the eye region – especially if there were festoons prior to your procedure. Sometimes topical steroid cream, or systemic medications such as steroids or diuretics can be helpful  in reducing the swelling more quickly. 
Another reason for bags after a laser to the eyelids  is the presence of underlying contour problems from the outset. If you had a depression below your eye – (the tear trough) -  or fullness below your eye – (prolapsed orbital fat) -  then a laser procedure is not going to solve that problem.  Only surgery  or volume augmentation can address underlying contour problems. Sometimes a laser procedure can accentuate the contour abnormality because it came appear more prominent relatively speaking because the skin is smoother. 
 Bottom line: consult with your laser provider further to understand your current anatomic state. Good luck!

If your laser treatment has been recent then it is probably a result of swelling after the procedure.  Keep your head elevated above the level of your heart and use cool packs intermittently.  Consult with your laser specialist if it persists.

The eye bags you are seeing may be from swelling.  The laser causes swelling which can mimick eye bags.  I would apply some ice to the area, keep your head elevated and contact your doctor if they don't improve.

It could be that you have some swelling after your treatment, which should resolve in a few days. Venus legacy treatments can give improvement. For under the eyes, I like a combination approach with lasers, microneedling/prp, and fillers. See an expert for a formal evaluation. Best, Dr. Emer

Laser resurfacing (whether ablative or non-ablative) and even YAG laser for periocular veins can all cause swelling of the eyelids, and it depends how aggressive the treatment was and what type of treatment modality.  The swelling can last about a week to as long as several weeks, and it typically comes down the quickest over the first week or two and then may taper off gradually over the next couple weeks.
Icing for the first few days, keeping your head elevated, arnica supplements, or even a short course of steroids (if very dramatic) can help the swelling come down quicker.
Best wishes,
Bradford Lee, MD, MSc