If your dizzy spells are when you are sitting up or just walking around, yes, I'd get a monitor to see if you are in AFIB....

Dizzy when standing up suddenly, is different...orthostatic mostly.
This is more like the autonomic symptoms. Sudden change in
position therefore is characteristic of autonomic issues. But autonomic can also occur when changes of position are not present.

When the atrium of the heart goes into a fibrillation state, the blood cannot be pumped out properly and fainting or dizziness happens. This can be when walking, sitting in a chair, standing.
This is risky because while the blood is stalled in the heart it may begin to clot, and then the clots may end up in your brain as a stroke.

So yes, I'd get tested. Some internists will do the Holter monitor but you can see a cardiologist too, for this. A cardiologist will most likely do a tilt table test too.