Can I raise my 7 ft living room ceiling

it depends on the thickness of the beams and how much you would like to raise the ceiling, you could do the job only if the beams allow or if they can be replaced with narrower beams

If it’s a false ceiling and there is a void then yes you could raise it but if not you’d need to take all the floors out and install a new floor at your desired height, but you would probably have to change your stairs and any services that could be in the floor space.

Your ceiling will be screwed to the joists above it. the only way you can increase ceiling height is to remove the joists and install them higher, this could be a significant job as your joists hold the 1st floor up. If your original joists are the correct size for which they span from wall to wall then you wouldn't be able to install smaller ones. if it's a old barn the chances are with modern joist tables you may even need to go bigger (but that depends on alot of factors)