If I lower my deductible amount, will the cost of my premium increase or decrease?

-Lowering your deductible, means that MORE of the claim is covered. That means your premium goes UP. It increases.Increase. The better question would be to ask yourself "what is the cost-benefit" of my premium increasing versus the probability of me having a claim and paying my high deductible?
Your premium will increase as you are assuming less financial risk.