She may be marking. Even fixed females will do that. I have a fixed calico that will sometimes back up against the wall and mark like a male would.
A new couch wouldn't have her scent on it and she may feel she has to mark it.
As far as peeing on towels or stuff on the floor, there is an easy solution - DON'T leave that stuff on the floor! I've found that with dirty laundry MOST cats actually seem to be prone to peeing on that kind of thing. It's like the musty scent of dirty laundry or wet towels elicits them to pee
. So I never leave that stuff where it can be peed on anymore.
With stuff like furniture, try putting her scent on it. You can actually rub her on it, and you can try rubbing her bedding on it (assuming it hasn't been peed on too). This works with some cats because once their scent is on the item they don't feel the need to mark it.
With her litterbox, try using several boxes with different types of litter and see which one she uses more often. Some cats are really picky with litter, and if she was an outdoor cat you just may not have noticed she had a problem with it before since she was going outside most of the time. Also scoop the litterbox and keep it very clean.
If you use an open litterbox try a covered one, and if you use a covered one try an open one. Some cats are actually odd about this. I have both covered and uncovered and my cats definitely prefer either one or the other.
Make sure to have at least 2 litterboxes, yes even with one cat. Some cats prefer to pee in one and poop in the other, oddly enough, so if they only have one and they poop in it they may pee elseware.