Adding to respond to BoyMom -- Most insurance companies do NOT consider pediatricians specialists unless they are in fields like "pediatric oncology." Regular pediatricians are treated by almost all insurers as "general practitioners" and you will be charged the regular co-payment, not a higher "specialist" one!
Original reply:
First, she needs to sleep, so if she sleeps OK on the floor and not IN bed -- let her sleep on the floor in her room. Do not make it a battle. Tell her it's fine so she doesn't have a constant feeling of "They're letting me do it but they don't really like it..." She must get real rest and it is not the end of the world, or of your parental authority, to let her sleep in a place that works for her. It's just not worth a battle.
Second, she does need a pediatrician and so does your son. Please get one, pronto. CareNow--if that's some kind of urgent-care walk-in clinic, they are not pediatricians, and you need a doctor who does all kids, all the time; an urgent care doc could be a fairly new one, or one without a lot of experience, etc. and they are dealing with everything that comes in the door; you truly need doctors who treat children all the time and understand kids' minds as well as their bodies. The entire metropolitan area in DFW just cannot lack ANY pediatrician that is OK. And the person to base your choice on is the doctor, not the receptionist -- a lovely, sweet receptionist is nice but not essential.
I would take her anxiety seriously. I have a girl who is 13 and has some anxiety (around school, not about sleeping) and I know that part of helping the child is acknowledging that there IS anxiety and not brushing it aside, not assuming she's faking it or "playing you," and never, ever belitting her ("You need to stop this silliness!"). Not saying you're doing those things yourself, but it is troubling that your husband sounds unsupportive; you need to talk with him about both of you taking it seriously and watching how you speak to her about it, so he does not go off on a "You're being a baby" tangent or anything like that. It's easy to do that in a moment of frustration! I know, I've been there. But the kid remembers it for ages afterward.
Yes, get her to see a counselor because this sounds beyond mere "I threw up once and now fear I might do it again" fear. Many, many kids go through this fear -- "I threw up in the car and now when I get in the car I'm sure I will again," or "I threw up when I ate a banana and now if I even smell it I know I'll do it again." Common, but most kids get past it eventually. It sounds like there are other, deeper fears about sleep and possibly nighttime, darkness, being alone, etc. going on here.
Please do not let your past bad experience with a psychologist make you avoid getting her some needed help. It sounds like your last one was a quack if he or she did not have your son talk about WHY he wasn't going to bed and just had him repeat a dumb phrase. Not all psychologists or counselors are like that, just as not all pediatricians are expensive, have mean receptionists or lack your insurance. Please be proactive about getting her help, or the anxiety may "generalize" and she could start to transfer her anxiety to other things -- like school, and that can be very problematic.
A pediatrician could give you a list of possible counselors and child psychologists to start with but you need a pediatrician first. And when she sees one, please be clear that this is NOT just about a "power struggle over bedtime." There really seems to be more going on here and if you focus too much just on "We need her to go to bed in her own bed" as the sole goal -- you may be missing a larger issue.
Has she ever seen her school counselor? School is nearly over here and already over in some places but you can still call the office and ask whether the counselor for her grade level can see you in these coming weeks (alone first, not with your child, so you can be really frank and so can the counselor without your child present). Then the counselor should be able to give you directions to find counselors in your area too.