Hi! Sorry to hear that your little one isn't feeling too well. However, if you just brought her into a new home, it isn't at all unusual that she's refusing to eat for you.
All Bearded Dragons are creatures of habit and routine, and they become very stressed when moved to a new home, with new people and new surroundings, especially if they're no longer babies. They find any changes in their lives very upsetting, and it may take at least a week or two for her to begin to relax enough to eat for you as she should. This is perfectly normal, so try not to worry overly much about her appetite right now, as long as she seems healthy otherwise.
You mentioned that she threw up all of her crickets.....were these crickets that she ate while she was in your care, or were these crickets that she ate before you brought her home? If she ate them while she was still with her prior owner, it could be that all of the stress of moving her simply upset her stomach and made her sick.
Beardies can get an upset stomach, or indigestion, just like people do, if they are under a lot of stress. If she ate the crickets after you brought her home, her upset stomach could be just from stress, or from the fact that her basking temps aren't up as high as they should be, in order to allow her to digest her food properly, or a combination of both.
My advice would be to let her stomach rest for at least 24 hours before you attempt to feed her again, just to make sure that, if she does eat, she doesn't bring everything right back up again. I would also advise giving her a 20 minute soak in very warm water, with some Pedialyte added to it, which will replenish any electrolytes that she may have lost from vomiting, and will also keep her well
hydrated. Even if she doesn't drink while in her
bath, beardies have the ability to absorb any fluid that their bodies need through their vent area, so giving her a long soak is an excellent way to keep her well
hydrated if she is refusing to eat for you.
If she seems frightened when you put her in the water, you don't need to make it very deep at all....as long as her vent area is under water, her body will absorb all it needs. Once her
bath is over, be sure to dry her well before returning her to her tank.
As far as the stress is concerned, once you get her rehydrated, try not to handle her too much right now,if you don't have to. Let her calm down and become used to her new tank and new surroundings for a few days. Its fine to sit near her tank and talk to her, so that she gets used to your voice and scent, or even to put your hand in her tank, but allow her to come to you, rather than forcing the issue by chasing her around trying to pick her up. If you talk softly and treat her kindly, she'll realize soon enough that you mean her no harm, and she should bond to you fairly quickly, given a bit of time.
As far as her tank temps are concerned, you need to get the temps on her basking site up to at least 105 to 110 degrees, in order for her to digest her food properly.
The lights that you are using are fine, but you may have to put some sort of a high basking rock in her tank to bring her closer to her lights, in order to get her basking temps up to that level. The best way to ensure that she has adequate temps for basking, in order to digest her food, is to invest in a digital thermometer with a probe on it. You can pick one up at any Walmart for about $12. Place the digital portion of the thermometer on the floor of her tank, on the cooler side. The temps there should be between 75 to 85 degrees. Attach the probe directly to the surface that she's basking on, so that you are actually measuring the temperature that is up against her stomach while she is digesting her food, and not the temperature of the air around it. The acual surface that she's basking on should be betwwe 105 and 110 degrees.
Once you get her stomach settled down, and she begins to relax and isn't so stressed, and you get her basking temps up to where they belong, she should be just fine in a week or two, once she's settled into her new home. In the meantime, please keep us posted, and if you have any other questions, or need further help, please feel free to ask, and all of us will be glad to help you, if we can!