You do not have an EIN if you have not requested one through the IRS. An EIN is usually only necessary if you own a business and have employees.
On a tax return you will only need to enter your Social Security Number if you have taxable income to report on the tax return. However, if you do not have any type of taxable income to report on the return, there is no need to file a return, with or without a dependent since you cannot receive any type of tax credit for the dependent if you do not have taxable income.
Unless you also received a Form 1095-A for your health insurance through one of the State Marketplace Exchanges or from healthcare.gov then you must file a tax return.
