when you gave her the time out and she hyperventilated, did she stay in time out, or did the fact that she was doing that freak you out and so she got out of time out?
in other words, are you letting her rule you because you fear her outbursts?
usually behavior like this indicates that you're not being consistent, that you're not setting predictable limits, and therefore the child starts to lash out at the world because she's trying to determine where the boundaries are, since it's not clear. this means you do have your work cut out for you, and it's going to be difficult, but you must must must get a handle on this. it's going to take strength from you. it's going to take kind, firm, consistent rules and boundaries. behaviors that are unacceptable shall not be tolerated. they result in a time out and if she screams and hyperventilates, so be it (she won't hurt herself; even if she makes herself faint, she'll resume breathing normally at that point, and it's not going to happen enough times to hurt her because you're going to be consistent and nip this in the bud, right? if you're worried, talk to her pediatrician.). make sure your time outs are effective, too: that means no interacting with her during time out. know that it is going to take you several months before things really smooth out, given her age and the level of acting out that you've allowed so far, but also know that you can do it!
from here on out, in all things, you need to set a limit, give a warning when she's pushing the limit, and then enforce the limit. always. do not say something, anything, if you're not willing to follow through. don't say "we're leaving the park if you don't come here right now" if you don't intend to leave the park immediately if she misbehaves. don't threaten what you can't or won't enforce. that's the most common thing you'll hear from a parent who's lost control: "Joey, I'm not going to tell you again, don't do that or we're leaving!" as mom then turns away to talk to her friend and Joey continues doing whatever it is he was doing, because he knows it's an idle threat. and then mom wonders why he never listens....
to get started, in a moment of calm, I suggest you sit down and talk with her, gently and lovingly, about the difficulties you're having with her behavior, and the fact that she needs to understand the rules. let her know what the rules are (no screaming, no tantrums, no throwing things, no hitting, whatever your rules are, but keep it to 3-5 rules to start) in simple, clear language. then let her know what the repercussions are (mommy will give you one warning and then you go in time out) and how that will work (when you're in time out, mommy will not talk to you and I expect you to sit in your chair for 2 1/2 minutes; the timer will not go until you are sitting in your chair, and if you scream at mommy or get out of your chair, then the timer starts over). let her know that you sense that she's been struggling and having a tough time, and you're going to help her understand the rules, because you love her and you want her to be a happy member of your household.
then stick to your guns, no matter what. a phrase that I read somewhere that has stuck with me is: your child needs to learn that she is very special and very important, but no more important than anyone else in the family. this means you must put other people first sometimes, and she must learn that failure to do so has repercussions.
good luck! it's going to take work (and both you and your husband need to be on board for this), but you all will be so much happier!