To file taxes you must have a social security or ITIN.
You can complete form W-7 from the IRS to apply for an ITIN if you qualify. Learn more and apply here: https://www.irs.gov/individuals/individual-taxpayer-identification-number-itin
If you are an independent contractor/small business, you are only required to have an EIN if you pay employees. You may want one to use instead of your SSN, but if you don't have employees your SSN is fine for a small business.
In Turbotax online, you would use the self-employed version. Create a schedule C to list your job income and expenses. You will owe self employment tax and income tax on the net profit from business. If you were paid cash or checks and did not get a 1099-MISC form. just report the income as "other business income not on a 1099-MISC." You are expected to keep your own accurate business records of your income and expenses. You can also add any W-2s, other income, your personal deductions etc. Your small business is included with your personal income and deductions on one overall tax return.