The cause of action in your case seems to be based on getting into the military. The military requires the medical records. If you are unable to get into the military because your medical records are lost you may be able to show cause and find a basis for recovering damages.
Sometimes you do not want a cash award. Sometimes you sue for an action to occur, and that may include compensatory damages to cover attorney fees,etc. People can sue someone for example to dislodge a building from encroaching on their boarders.
You would at lest be suing for recovery and reconstitution of your medical records.
I am familiar with the MEPS and what is important is diagnosis. All of your lab and x-ray reports if any are recoverable. All diagnosis are recoverable through the records maintained by the billing offices and insurance claims processing centers. So it is possible to reconstitute this record sufficiently to allow you to enter the military.
The MEPS also will allow or should have allowed you to get a full physical at your own expense confirming your existing or prior existing medical history and prognosis. (per my retired army first sergeant friend).
Under HIPAA you file a complaint about the lost records, they are investigated and fined and can be forced to reconstitute the record,etc.
Under a civil law suit, you can sue to force these things,and if you can fix a money loss, to recover those damages.
It would be a long shot to expect money damages for college, because you have not been accepted into the service. BUT if you can show that you were denied entry into the military, because of the lost records, and you can prove that except for that, you would have been let in, then perhaps you just might then be able to fix money damages to the extent of the military contribution to a college fund had you been in. Its a long shot, and no guarantee.
also if all it take is reconstituting the records to get you in the military, then the court may order the case into arbitration and allow the clinic time to do that.
You would have to sit down face to face with a local attorney to discuss the merits of such a case.
at the very least, you can file a HIPAA complaint and force a reconstruction of the records.
Find an attoreny who processes medical malpractice or medical disability;if they also have experience with military and veterans that is good too.