You must have done something more than change the name of the table or this would not happen. (Changing a table's name or a table occurrence's name alone won't break the link between the fields on the layout and the table occurrence selected for the layout.)
Did you by any chance change the name selected in "Show Records From" in layout setup?
Did you delete a table occurrence "box" in Manage | Database | Relationships?
I'm not really sure what I did, I just know I was trying to set up a new table and "experimenting" with things and that was the end result. Can it be fixed?
Open Manage | Database | Relationships
what do you see in this window?
Do you see a "box" for your table here?
Well, there was 3, but I was able to delete two of them without any problems. The only table now is called "data file" and when I click on the "data file" it shows all my fields are in there but it names the table as Physican Specialty (with all the fields and records) and another table under it that is also called "data file" with one field and no records. Can delete the data file with one field and one record and then rename the physician specialty to data file without loosing my fields or records?
Deleting them is what may have messed up your layouts...
In Manage | Database | Relationships, you are not creating or deleting tables, you are working with occurrences of the tables you've created on the tables tab. Think of these as "labels" for your existing tables used so you can link them in a variety of different relationships. Your layouts link to one of these occurrences in Show Records From in Layout Setup... (Enter layout mode and pull down the layouts menu.)
If you delete a table occurrence here that is listed in Show Records from for one of your layouts, it looses it's "link" to your tables and all the fields pop up with the "Missing" warnings that you are seeing.
To learn more about table occurrences, you may want to take a look at this tutorial thread: Tutorial: What are Table Occurrences?