Brief Answer:
Should be urgently checked for possibility of stroke.

Detailed Answer:
I read your question carefully and I understand your concern.

Such symptoms as you describe can be related to a stroke, damage to a brain area due to blockage of the supplying blood vessel. In your case the area likely to be involved would be the cerebellum or little brain as it's called, responsible for balance and coordination.
Looking at your age I would say that it makes you someone who is at a high risk for stroke. Since stroke is a condition which is threatening and can cause disability, it is important that you get to the ER as diagnosing and treatment in time can be life saving and avoid disability.

Another possibility is an inner ear issue which is also involved in balance. It is not a threat such as stroke. However as I said at your age when there is a sudden neurological symptom such as balance issues it is imperative to exclude stroke before passing to other diagnoses.

I remain at your disposal for further questions.

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Brief Answer:
Read below.

Detailed Answer:
Thank you for the update.

There is no clear cut answer to your question as a small stroke or TIA (transient ischemic attack) may improve but still needs investigating regarding the cause, in order to prevent recurrences. So while improvement is a good thing and makes going to the ER less urgent, I still feel your should be evaluated sooner rather than later if not at the ER by your primary physician.
General dizziness can have many causes but it is that veering to the left which has me worried as it is a focal sign and would make me more comfortable if you were evaluated.

Let me know if I can further assist you.

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