Tantrums

I'm sitting in my lounge feeling like the WORST mother ever in the history of mankind right now. My little girl, almost 15 months old now just had the worst tantrum yet and where did this take place.... in the bath, her hair full of shampoo, her body very slippery with aqueous cream soap which meant I could not simply abort the whole bath thing as I had to rinse her first which just blew the whole thing into an even worse rampage. She wanted to get out just all of a sudden and despite thinking "should I just take her out as is and let her lie in her cot full of soap, shampoo and soaking wet while she gets over this", I persisted and rinsed her off and only then took her out of the bath. It was a nightmare!
I had to grab tightly under her arms to stop her from thrashing and falling out onto the very hard and slippery tiled bathroom floor.  Once I had her safely out the bath and was trying to wrap her safely in a towel I immediately saw red marks under her arms where I had held her so tightly. I tried to calm the whole situation down and soothe her but she lashed out and hit me over and over in my face. She looked to me almost possessed! I had to hold tightly to her little wrist to stop her hitting. She just wouldn't stop so I put her down on the floor away from me as I'm sure holding their wrist tight like that can cause pain and bruising surely!?!? Oh boy, that was almost worse then. She threw her head down onto the floor and was screaming so much she started going purple all over and looked as though she was temporarily not breathing!

I tried to just touch her back and stroke her but she thrashed more. I blew in her face to make her catch her breath. That helped slightly.
As soon as I could see a gap I picked her up and went down to her bedroom thinking if I can just get her to the safety of carpet and a pillow at least she wont hurt herself but the thrashing and screaming continued.
I decided let me just push through and get her nappy on and dress her and then I can try to hold her and give her bottle and just calm the whole thing down.

It took ages and some shouting on my part out of sheer frustration and even fear. she just wouldn't wouldn't wouldn't calm down at all.

Eventually I managed to get her onto my lap on the couch in her bedroom and she finally took her bottle and that calmed her. I held her after she had finished feeding but I could sense she was very very very distraught still.
She let me put her into her cot and she rolled over to the side like she does when tired so I covered her and left the room.

She has not made a sound since. I presume she has fallen asleep. I'm devastated. I feel like I have just abused my child. What makes these little people suddenly so angry and out of control? I'm wondering what I could have done differently? Perhaps I must always have a huge towel in the bathroom ready for if this happens again and just take her out and put her on that and step back until she calms even if she is covered in soap. The tricky part is getting them out the bath when they so slippery and not hurting their little under arms.
Gosh no man I just feel horrible horrible horrible.