Among the symptoms of Vitamin D deficiency can be muscular pain. Vitamin D supplementation has been shown to reduce the severity of asthma attacks, but to say that deficiency can cause lung disease may be a stretch. Given how Vitamin D is utilized by the body in metabolic functions, it may reduce the potential involuntary muscular force of the diaphragm, which may lead to shortness of breath.
I hope you mean 6,000IU, not 60,000! Doctors may prescribe shots of Vitamin D that amount to 50,000IU, so a single dose amounting to 10% of that is not problematic. That said, you should not be supplementing in the amount I believe you are describing without a doctor following your blood serum levels. Vitamin D is not only a vitamin, but serves a dual role as a pseudo-hormone, so manipulating serum levels with a dosage such as this would not be recommended.
My first suspicions would be elsewhere to diagnose dizziness, but I know nothing about you or possible medications, etc. Best wishes!