If you already went to the ER, a walk-in clinic is not going to provide you with any more in-depth answers. You might as well follow-up with your family doctor on his/her return from vacation.
Having said that, if your symptoms worsen (nausea, vomiting, fainting, worsening vertigo/dizziness, double vision, difficulty producing speech, difficulty swallowing without choking, loss of use of your arms or legs, etc.), go right back to the ER.
Any testing the ER staff feel is necessary will be done on that visit. Any similar testing that a walk-in doctor wants done will take weeks to months to arrange, or they will tell you to go to the ER themselves.
I'm surprised the hospital you went to didn't do a CT or MRI when you were there. But if your neurological scan tests were normal, it likely wasn't necessary.
Always disclose all health information to any doctor or nurse examining you, including drugs/medications, history of recent injuries, etc. Not doing so can lead to a useless guessing game of cat and mouse that wastes everyone's time, can be harmful (to you) and may lead to unnecessary tests. They'll also think you're a nut and won't take you as seriously if you start withholding information (e.g. that you had sustained a concussion recently)
As for the concussion that you mentioned, how long ago did it happen and how severe was it? I'm inclined to think that your vertigo/dizziness may be the result of it. These symptoms can last awhile. Has anyone tried the Dix-Hallpike Maneuver on you yet?
Also, inner ear infections/problems do not always show up on testing, even on CT or MRI. Any significant brain injury would have revealed itself during the neurological screening tests.
If all your testing comes up negative, and your vertigo persists, your next step is a referral to a Ear-Nose-Throat specialist, or neurologist.
They'll do hearing tests and Caloric Vestibular system testing on you (the latter is NOT fun).
Hope that helps.