Hi and welcome to the forum.
The first thing that you need to do is regain her trust and prove your leadership. Start with her loose, walk to her, if she walks away or doesn't acknowledge you, just give her a little push and follow behind her. There is no sense in making her run around like crazy, that just adds stress to the situation for both of you. Just walk along behind. The only way that she is allowed to stop is if she gives you her complete attention, both eyes, ears, licking chewing, etc. When she starts to offer this, just stand there and keep your eyes on her. Stay quiet in your breathing. You may be 2 or 20 ft. away from her at this point, but just look for the connection. If she approaches you, it must be polite, stopping at least an arms way away from you and without any negative signs of ear pinning or anything else like that. When you lose the attention, start approaching her again, when you get her attention, stand still. If she is truly paying attention to you and not walking off, then stand patiently and wait for a sign from her that she is letting her defenses down (yawning, licking and chewing, sneezing, dropping head below the withers). As she starts to achieve this relaxation with your focus on her, go ahead and approach. Don't be sneaky, just walk up to her normally. If she leaves, then you follow. Stop when you get within arms reach of her and offer your hand for her to sniff. This is another test to see if she will be pushy, or polite. Any pushiness from her results in pushing from you. Only when she is quiet and relaxed, reach up and stroke her in between the eyes. Give her a scratch, spend some time just being a horse with her, then, when you have her full attention in a calm relaxed manner, walk away. That will be the end of her session for the day.
After doing this a while, making sure the horse is truly "caught" not just "haltered", she will start coming to meet you again. Now remember, you are not trying to make friends, you are trying to prove that you are a strong yet fair leader. If she shows any signs of wanting to leave you, let her leave and just follow her around. Don't let her stop unless she is stopping with her attention on you. This can take a long time at first, but will become shorter each time, and its good exercise for you anyway. I have found this much more effective than chasing them at higher speeds,since the horses frame of mind stays calm and doesn't jump into the fear/chaos mode.
Once she has truly achieved this, then you can put the halter on. Be very specific about her manners, where she stands, not letting her move if you put her feet in a place, etc. Most importantly, your personal space is sacred and you can do whatever is necessary to protect it. The pushier the horse, the bigger and stronger my personal space bubble is. This is for my own safety. I've handled horses before that I would let get any closer than 12' away from me to lead them to a stall. As the horse learns manners, my protection goes down, I let the horse move in as I feel safer with them. Any threat to my personal space is met quickly, strongly, and assertively, but then I must be able to go back to complete neutral as soon as the threat has retreated.
Now that the horse respects you on the lead, you can progress with your basic skills. The vet is a learned skill that many people only think about when the vet is there. For me, I see it as my job to prepare the horse for the vet or farrier. Start by yourself, holding the horse in hand. rub the mares neck, where the shot would go. Keep rubbing until she achieves that state of complete relaxation again. Another trigger is the smell of alcohol, so go ahead and wipe alcohol on her neck, again, until she is completely relaxed. Once she is to this point, where you can rub the injection site with alcohol without her head being up above the withers and without her feet moving, then use a toothpick and touch it to her neck. Move with her if she moves, do not increase pressure, keep it constant and soft until she stops moving and relaxes, then remove the toothpick. Go through the process again and this time use the toothpick a little harder. No, its not comfortable, but its a fact of life, and if the horse learns to relax during this process, then it will be a lot easier on them and on the vet. If done properly, your horses reaction to the toothpick will be minimal. Once she is used to this, you may want to try again with another person either holding her or using the toothpick, since that is one more thing that changes when the vet is there, you are basically recreating the situation and teaching her to relax through each step of the process, resulting in complete overall relaxation and acceptance. I have used this on horses before and it does transfer easily to the *** of a needle.
It is very important that you establish your most basic ground rules first, for your safety and her sanity. Whenever you have a problem, back track to the beginning and figure out where it went wrong. Once you reestablish your position as leader, she will be more accepting of other people that you introduce to her as well. You were very right not to ride her in that state of mind, however, I probably never would have even tried lunging until the leading was not only solid in obedience, but also in the state of mind. Remember, we can't always set the agenda for our horses, determine the goal when you see what the day throws at you. The more that you can build your horses trust through new obstacles without throwing her into fight or flight mode, the more solid and trusting companion that you will have. Hope this helps, good luck!