I would definitely check with the chiro and your saddle fit. But the tail swishing may also be from you using too much leg or not taking your leg off soon enough after asking for the trott or lope. My mare is very swishy with her tail also, so to keep it to a minimum in the show pen, I click to her for the trot and for the lope, I move my leg back, and kiss.
Now she doesn't mind that I am holding her with my legs, so she doesn't get lost on the straight lines, but it is the transitions that she gets picky with. I realize she may need to "just get over it" but this is how she is and she is really, really good at her job - western pleasure, so I am not going to fight with her over this issue. If she doesn't want a lot of leg on her, fine with me.
Now my other horse, lazy, lazy, lazy. He's more like, "huh, you wanted something mom?" And I'm like, "sorry to have woken you up." Best darn trail horse at 3yrs. Old, but I bred him to be a dressage and jumper. I'm trying to convince him about what his job is supposed to be.