Upvote:2
There are public showers at Emirates Terminal 3, just look for the signs. There are multiple lounge options, but all are on Terminal 3. Terminal 2 only has one lounge, but it does not have a shower. There are no public showers in Terminal 2.
Here are your lounge options:
The Marhaba Lounge (paid access or complimentary on some credit cards, showers are extra). Marhaba also operates the lounge in Terminal 2. You can book them online via Loungepass here.
The Emirates Business / First Class Lounge - these offer showers and spas; but are expensive if you are not an Emirates Skywards member. The rates are listed on Emirates' website. Emirates lounge are only in Terminal 3 and Terminal 1.