I have hyperthyroid. I am taking neo-mercazole. The issue is while on medication I cross the TSH level and get hypothyroidism. How should I keep track?

Lower the dose. If you become hypothyroid on the pill, you need to decrease the dose until you are euthyroid again. Your doc should be able to do this for you. This is the art of medicine. If the pill is unable to do this, you might need to consider definitive treatment such as i-131 ablation...