Is it usual that eyelids cannot open for a period of time after upper and lower eyelid surgery?

It is normal for the eyes to become swollen and to bruise after upper and lower eyelid surgery. This can make your eyelids heavy and feel like they can't open well. Ice can help with the swelling. I usually ask my patients to ice for 20 minutes of each hour while awake during the first 3 days after surgery to minimize swelling. 
All the best, Dr. Brace

However, eyelids can swell and be heavy.  If the surgery is done correctly, this will not be a problem.  The challenge is eyelids with preexisting ptosis that is not corrected with blepharoplasty.  Swelling can actually exacerbate the ptosis.  The solution is to recognize the ptosis and correct that at the time of cosmetic blepharoplasty.  Unfortunately this seems to rarely happen because the majority of blepharoplasty surgeons often don't know their anatomy once they get a few layers deep into the eyelid.