Can shingles normally on left shoulder, but without an outbreak right now, cause the arm to go numb and cause dizzy, light-headedness?

No: Shingles affects only one nerve root. The places you are having problems involves multiple parts of your nervous system. Although someone who has recurrent shingles might have some symptoms when the shingles are not apparent, they are gennerally much less than during a flare, they are still limited to the same nerve root distribution.

Shingles can be very: bad. Vaccination is great but now it is probably too late. Check with your doc to make sure nothing else is going on. You may also benefit from medication and there is no need to wait. Check with your doc. All the best and good luck.

Maybe: If shingles was the reason for the numbness, I would have expected there to be numbness at the time you had the rash. Other things can cause the arm to be numb, even sleeping on it wrong. There are other rare causes, if it lasts and lasts you should clearly get it evaluated. If it comes and goes, changes it is not as serious. A detailed neuro exam and good physical should help evaluated it.