Interior clear span 16′ header size

As @TheEvilGreebo mentions, 2x6 is not enough for a floor that will be used as "habitable space". I know because when I remodeled my attic to convert it to a bedroom, the existing 2x6 floor joists (over a very similar span) were not enough and I had to sister them all.

At a minimum you will need to check with your local (municipal or county) building department. They should be able to tell you what you need.

It might be easier to get a structural engineer or architect to come out and tell you what to do. If they are not drawing up plans you might be surprised that their prices are quite reasonable (they should be able to give you a quote for what it would cost for them to come out and generate a report up front). It will also help when you get your building permit to be able to submit the report written by a certified professional to the building department.

If you put a beam across the room you'll feel bad every time you look at it. if you have a flat ceiling, you'll feel proud.

Use joist hangers to put some 2x4s between the ceiling joists so that they pass just above the 2x6 (stuff's going to sag), drill through the top plate from below with a spade bit and screw the 2x6 to the 2x4s remove the wall and top plates patch and plaster the ceiling.

If you can't get into the ceiling to get enough access to fit the hangers you could just lay 2x4s across the top of the ceiling joists and use really long screws, or maybe even come through the roof with threaded rod.