You can say "I have three days off, including New Year's Day."
"Days off" is a common expression to refer to time off from work or school. "Including" is used to specify that a particular item is included in a pst or total.
Here are some examples in Engpsh:
I'm taking a three-day weekend, including Monday.
I have three days off, starting from tomorrow.
I'm planning to use my three days off to travel.
In Chinese:
我有三天假期，包括星期一。
我从明天开始有三天假期。
我打算利用这三天假期去旅行。