Hi can tight neck muscles cause dizziness and balance problems?

Very doubtful. A neck muscle problem primarily would not cause dizziness or balance problems. However, problems with your spine could cause both balance problems and neck pain. Dizziness would still be a separate issue.
Might. Yes possible , if for any reason compromise the cerebral circulation by pressing the carotids.

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Is it possible that tight neck muscles can cause eustachian tube problems?

Tight Neck Muscles. Yes. This is quite common. Pay attention to your sitting posture during the day and avoid straining the neck muscles. Try an otc "heat" creme to the tight neck muscles and a short course of any decongestant, assuming you are not on blood pressure medications. Read more...