i think between normal ceiling fan versus ceiling fan with a lamp,
in term of coolnees, they are same but or probably fan with lamp has less "air" because this type of fan mainly used for it's look, rather than functionality.

in addition, lamp from the fan cannot beat your ceiling lamp, especially considering you're using 2 lamp to light up your living room.

Maybe, what you need is an extra fan to cover all the area in the living room, but you must rearrange both fan so they are evenly separated.

Or, you can add an aircond

Another thing, how old is you fan... all new fans nowadays are much faster compared to and old fan..