I honestly don't think you did anything wrong. If you accidentally hurt a parrot (accidentally touch a sore pin feather, for example), they'll sometimes let out a yell of shock and pain to let you know that you hurt them. When I was teaching Noah to be gentle... if he bit me (he was obsessed with chewing on my fingers), I'd get his attention, give him a stern look, and ask him to be gentle in a calm voice. By doing that, I gave him a chance to correct his behaviour, and I wasn't blaming him or telling him he was "bad" (I just wanted to point out he was getting a little rough, but that I wasn't angry with him. It wasn't his fault, but he needed to stop). If he proceeded to chomp down again less than 10 seconds later, I'd give him the evil eye, tell him he was "bad" in any angry(ish), stern voice, and I would set him down, and turn my back to him, ignoring him for no more than a minute. He found it absolutely devastating when I'd ignore him and would start calling to me and would fly to me, pleading for me to forgive him and acknowledge him. After he had time to realize that biting means we don't get to play together, I'd tell him that I forgave him, and that he better be a good boy next time. Then we'd resume training and stuff.
I think it's very important to let them know that you aren't angry with them, and that you aren't punishing them. If you make too big of a deal out of it, or keep laying into them about it after the fact, it can make them angry and hurt their feelings. Sure they bit you on purpose, but it wasn't malicious. Odds are, they weren't really thinking at the time, and weren't trying to hurt you. Overreacting to a mistake or a test bite can make them angry with you. For example, when I was younger, I accidentally gave my friend a little scrape. I totally didn't mean to, and felt bad and was about to apologize, when she flipped out and started yelling at me and going around, telling everyone how I'd hurt her on purpose and stuff. At that point, I didn't feel bad anymore, and I definitely wasn't going to apologize. I just wanted to break her nose. I didn't beat her up, and probably wouldn't have, but this is a good example of why you need to let your parrot know they did something a bit naughty, but then move on. You let them know they made a mistake, they probably feel bad and embarrassed, and by letting them know you forgive them and aren't going to hold it against them, they learn from the experience and it helps to strengthen the bond between the two of you.
Make sense? I have a unique insight into the minds of parrots because of my excellent memory. I remember a lot of my childhood, and what I was thinking when I did something "bad", and how the reactions of others made me feel, and how it affected my behaviour. I remember that whenever I misbehaved, I did so without thinking. I did things without thinking (odds are I was thinking about having fun), and oftentimes I realized I'd messed up as soon as I said or did something "bad". When people would get upset, it made me feel bad and I'd become angry and retaliate. When I did do something bad on purpose, it was either because someone upset me, or because I was having a mood swing and wasn't in control of my actions. I imagine it would be exactly the same way with parrots, so I treat them in the way I would have liked to be treated.
The fact that she stopped biting when she realized she'd hurt you when she gave your arm a welt, is what you want. She was thinking, "Hey, I want some attention", so she gave you a "little" poke. But when you yelped, she realized she'd hurt you and felt bad. The way she responded afterwards by being quiet and going onto your shoulder is her way of apologizing. She didn't mean to hurt you and wanted to be forgiven. The only thing I might have done differently is I would've let her know that you understood it was an accident, and that you forgave her. It was good that you didn't give her a timeout. Timeouts should only be given if the bird refuses to modify their behaviour after being made aware that you don't appreciate the behaviour, and continue to misbehave after they've been given a second chance. If you'd given her the timeout, you would've been punishing her for apologizing and being good. This would've made her feel really bad about herself and could've caused anger and resentment towards you, so it's good that you accepted her apology and moved on. She'd learnt her lesson, so no need to beat a dead horse (or however the saying goes).
Noah behaves not because he fears the consequences of not doing so, but because he loves me. Every time he steps up for me, he doesn't do it because I'm forcing him to, but because he loves and respects me and knows that these feeling are mutual. If he's eating some really yummy food, he might not step up for me right that second, but if catch his attention and ask him to step up for me, he'll step up without making a fuss. I never force him to do what I want and always give him a choice. But 9/10 times, he chooses to do what I ask since our relationship is based on love, respect, and the right to choose.