At 15-16 miles and if the channels look OK on the closest TV even after splitting, it sounds like the antenna is doing its job.
A distribution amp sounds like it would work better than bigger antenna. It doesn't sound like you need much amplication, but if you;ve got a decent SA amplifier already I;'d try it first. Either split the signal and amplify the leg before it enters the cable jack or you can try amplifying the antenna signal and then splitting.
At 15 miles and 15dB amp it might just overload the tuner on the closest TV, but you can try both ways and see which works best. If you already have the amp, that;s certainly the cheapest/easiest route. If it doesn't work well, then the other options are still available.