As a self employed person, you will file schedule C to report your business income (and expenses). You will also file schedule SE to pay your self employment tax. The IRS shares the info on schedule SE with the Social Security Administration and that is what gets you SS credit.
Even if you could make a case that the teaching income was a business, the room and board (for a temporary out of town job) is business expenses. After deducting your expenses, you have zero income. So you cannot get any SS credit, for the activity. You’re not allowed to forego claiming expenses to get a tax or SS benefit.
