Daughter Impulsive Emotionally Dysregulated and Needs a Timely Assessment

I congratulate you on helping your daughter face her issues. I'm going to make the assumption that her social issues have less than severe consequences in that she is not about confined by authorities. If that were the case having her evaluated in an psychiatric emergency department would be the first step. 
Given the complexity of her issues, I recommend you find her a clinic where she can see a team of mental health professionals to enable a full range evaluation. It generally makes sense for her to see a therapist to start. Then if psychological testing or psychiatric consultation is in order, it is readily available on the team. This sort of setting can be found in most multidisciplinary mental health clinics.
The other rule of thumb I often use is that therapy or all forms of treatment should have had some effect after 6 sessions. That could mean 6-12 weeks. Your daughter should feel it's been helpful. You may not see that help except in her comfort level and evidence of new skills she's trying out.
If the time investment seems too risky in that there could be more serious consequences, I'd suggest seeking a partial hospital program to get a jump start on treatment with an intensive program. Such programs operate daily, all day, and she would be seen by a psychiatrist at least 3 times a week. An intensive program allows a complete evaluation and time to try a number of treatment approaches so as to ensure some quick progress and a good aftercare plan.
I wish you and your daughter the very best.