Yes, in 99% of cases the problems should go away with acclimatization. But seek medical advice if they persist. The two are not unrelated. Anyone who has experienced vertigo knows that nauseau and vomiting are induced by serious upsets to the ears' balance mechanism. And there can be physiological causes for eustachian problems.
The body changes with advancing age, uncorrected ear maladies can become chronic in a few cases. In the worst scenario you could lose your medical.