One eye is hooded and the other is not. Can I have a blepharoplasty on one eye? (Photo)

A blepharoplasty would not correct your problem.  It appears that
you have right eye ptosis.  Ptosis may be
present at birth (congenital) or caused later in life (acquired).  It is caused by weakness of the levator
muscle that is used to lift the eyelid.  A formal evaluation is essential and
you are likely a candidate for ptosis repair. 
I recommend you consult with an oculoplastic surgeon or a facial plastic
surgeon who is experienced in ptosis correction.

Your photo demonstrates a ptosis , or drooping of the right upper eyelid. In a young person this is most frequently present from birth or congenital, although there are other causes. The muscle that lifts the lid is either stretched or positioned too low at rest. If the muscle fuction is otherwise normal , this can be corrected by a simple procedure. This is not a blepharoplasty, but is done through the same incision. An experienced surgeon can determine the cause and appropriate treatment.

The right upper eyelid is more droopy then the left but if the right side is fixed without attention to the left side, after surgery, the left upper eyelid will look to heavy.  This is known a Herring's law ptosis.  One of the posters here suggests a Mueller's muscle conjunctival resection ptosis surgery.  This is a very popular surgery with eyelid surgeons but it has a high of only partially addressing the upper eyelid ptosis.  It also will not address another issue that you have which is upper eyelid lash ptosis.  You have no support in the eyelid for the upper eyelid lashes.  An anterior approach, levator resection ptosis surgery will create the opportunity to correct the ptosis and also address the upper eyelid lash ptosis with an anchor blepharoplasty.  I recommend getting the right surgery the first time.  Also, in my opinion, most people benefit from light intravenous sedation rather than just having the procedure under local anesthesia.