I took EK from JFK to DXB with a rolly-bag, backpack, and CPAP machine (medical device!) knowing that i was going to have a long layover in DXB. The CPAP is approximately the size of a big loaf of sourdough bread.

The nice (but firm) lady from EK supervising the check in counters made me check my roll-on bag as she said that the backpack was my carry on and my CPAP was my "personal item." Not a big deal, just shifted some stuff around and checked in my bag. AFAIK, there is no equivalent to the Americans With Disabilities Act in the UAE, thus the treatment I received.

Therefore, I would expect that you would be asked to check one item of your three.