The whole field of cerebral ischemia is classified into a number off different stages, including TIA, PRIND, PS and CS. The severity is different, as are clinical symptoms.
The TIA or trasitoric ischemic attack is classified with symptoms that fully recover within 24 hours. That is what you have mentioned.
Next level would be a PRIND or prolonged ischemic neurologic deficit. That lasts longer than 24 hours, but symptoms return to full normal.
The progerssive stroke (PS) has increasing symptoms over a period of 4 weeks, symptoms are not fully reversible.
And the completed stroke (CS) has chronic neurologic deficits.
So from that definition you did not have a stroke. Nevertheless, if looking at MR images, you will see a focal loss of brain tissue (in your case half the size of a peanut), and radiologists usually will describe that as 'compatible with a stroke' or as a 'lacunar stroke / infarct', which is a bit misleading, as the definition of a stroke includes a permanent loss of neurologic function. I think, this is, where this disagreement of diagnosis originates from.
Sending somebody home from the ER with a stroke I would consider as a mistreatment, as with a stroke you have a significant area of the brain with inadequate oxygen supply. Depending on the duration, one would need to do everything possible to make this region as small as possible. But with a TIA, this is different, as the neurologic deficit is short lived. Protection of further events and search for the culprit is the adequate way to go.
From my perspective, calling it a stroke will not have positive effects on your ability to regain your medical, as physicians might associate something different with a stroke than with a TIA. That is why I was so clear in pointing out that it was not a stroke.
The good thing with a TIA is, that it was so small and the amount of brain tissue involved was small enougt, that plasticicity of the brain was capable of rerouting the nerve-cell function of the area, which got lost to other cells, and function is 100% back. So no lasting residuals. Therefore, the TIA really just is the wake up call, and it is never too late.
I have to add one information, I forgot in my recent comment. The percentages for stroke risk over time after an TIA are for untreated patients. Treatment has shown to be effective to reduce these numbers.
To your question with PFO. I am not absolutely sure what you mean, but if it is a patent foramen ovale, the easiest test would be a contrast enhanced echocardiography. With echo you could also look for thrombus in the atrium and for the aortic root, but for the latter there could be the need for a transesophageal probe position (which sounds worse than it actually is).
Alternatively, you could go for cardiac MRI to look for the left atrium, an assessment of the foramen ovale as well as the aortic root. Unfortunately, you need a high end MR scanner and somebody who is trained in cardiac MRI.