It may just be that, like most toddlers, she'll need you to "stay the course" for awhile on one consistent way of handling the hitting and kicking.
The words you are using with her are pretty much what I use for the same situation (addressing the emotion and so on). Giving her a good solid alternative can be helpful also... perhaps hitting a pillow just isn't helping her to release those very strong emotions? Maybe something with a little noise? I usually tell DS to go and give his drums a good whack and this seems to help. If kicking is the order of the day, change the scenery, get outside and kick a ball until she's pooped!
I'm by no means an expert--always revamping (and hopefully bettering) my discipline style, but I do keep in mind that with everything toddler, it does sometimes take many
repetitions before the ideas begin to sink in. With that, I just keep my responses consistent and calm (as possible, that bite hurt!) and wait...
On other thing I've done if the hitting or kicking (in our case biting) did actual physical damage to the other person (in this case, yours truly), is just be honest, "OUCH, that really hurts, the skin is broken, I'm bleeding... " Then I had him accompany me while I tended to my wound. Everytime he saw this wound over the next few days, he'd get a very sad face and say, "ouch." It broke my heart actually. I didn't want him to feel monumentally bad for a farely run of the mill toddler behavior, but it was nice to see some understanding on his part.
The biting thing was short-lived and remember most toddlers go through stages like this, and most get through them sooner rather than later.
Hang in there.