Can 14/3 wire, with all three conductors hot, be the only cable in a switch box?
It's better (and to code for new construction) to run a 14/4 wire to get a neutral to the switch. In case you want to upgrade it to a smart switch or timer that needs that neutral.

You could leave the 14/2 in place as the unswitched feed and run a new 14/3 in parallel to carry the switched lives. However when you do so you must ensure that the neutral goes back to the through that 14/3 and that the lamp/fan is connected to that neutral and not the one feeding the 14/2.