Dear Elizabeth,
In addressing your inquiry I hope to convey information helpful to others who may be seeking entry experiences, too.
There is not much information here that would inform a potential networking contact that he or she could be helpful to you. Think of potential contacts as customers whom you can serve by meeting their information needs. Here are some key information items that would enable someone to respond effectively.
When are you moving? What field do you want to work in? Will you work as a volunteer or do you expect to be paid. Will the internship involve coordinating with your academic faculty and require reporting? Do you have prior work experience? Do you have prior healthcare experience? Do you have a resume you can provide?
I suggest you make contact with the ACHE chapter serving affiliates in the Dallas region to assist in your efforts. By far, it would be best to actually attend one of their events to make face-to-face contact with Dallas area healthcare executives.