do employee's get new sick days starting at the begining of the new year?

Every company has different benefit plans. You need to ask your Human Resources department about the company's sick day policy.

do employee's get new sick days starting at the begining of the new year?

Paid sick leave benefits are not required by law. Unpaid sick leave, however, may be legally required if you are subject to either federal or state family and medical leave laws. Sick leave, like other time-off benefits, is valuable to employees and, when combined with certain disability insurance benefits, can create an attractive package of benefits that make employees feel secure and valued