Brief Answer:
Stroke consequences more probable.

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

I might be able to be more sure in my answer if you were able to provide some medical report on those strokes, perhaps the CT or MRI imaging report so that I might assess what areas of her brain were affected and to what extent.

A stroke means that an area of her brain has been damaged. Luckily in your mother's case the damage hasn't been too serious but still 3 strokes could be leaving some residual deficits like balance issues and memory impairment. So that would be the most likely hypothesis. There is not a specific treatment to reverse that damage, if memory impairment is prominent drugs used for dementia like donepezil or rivastigmine are tried, but their benefit is limited.

However if the symptoms have developed only recently, having been symptom free after the strokes, other causes have to be considered. One possible cause for her dizziness might be problems with her heart especially with her overactive thyroid which is a major risk factor for arrhythmia. So a cardiac evaluation would be necessary.
Also some routine blood tests are also indicated for metabolic changes such as complete blood count, blood sugar, liver and kidney function tests, electrolytes, vitamin B12 levels, monitoring of her thyroid function.

As for prevention of recurrent strokes as your neurologist said treating hypertension and hypercholesterolemia is important. However if hers was an ischemic stroke then a blood thinner is indicated. There are two major groups antiaggregants like aspirin or anti coagulants like warfarin. Which to choose depends on the cause of the stroke, warfarin is preferred when there is a heart arrhythmia at the origin of the stroke, if you are not sure about that that cardiac evaluation I mentioned is even more important.

I remain at your disposal for further questions.

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