Hi, I understand your concern and I'll try to help you. It is not usual to feel those dizziness and even have difficulty walking after a head trauma. Furthermore, faintness description is compatible with a clinical condition known as syncope and necessarily need a thorough investigation.
There are several causes of dizziness such as cardiac, and by 
brain damage and dysfunction of the 
vestibular system. Cardiac causes are more common in older people (I do not know your age) and originates arrhythmias such as 
atrioventricular block, supraventricular and ventricular tachycardias, 
heart valve disease. Brain disordens constumam occur after trauma with immediate bleeding as 
subarachnoid hemorrhage or late, as chronic 
subdural hematoma, and cerebrovascular diseases such as stroke. On the other hand, the dysfunction in the vestibular system constumam be the most common causes of dizziness and the most common is benign paroxysmal positional vertigo.
Clinical data you reported are not sufficient to distinguish what the real cause of the dizziness. But you had a 
head injury that can cause intracranial bleeding late as chronic subdural hematoma and this needs to be discarded. In addition, it is necessary to rule out that you are not some kind of arrhythmia or other heart condition.
So I suggest you return to the emergency room for a reassessment. Thus, we can discard the dangerous causes of the clinical picture you reported.
Hope I have answered your question. If you have any further questions I will be happy to help you. Wish you good health.