Self employed

No, you generally are not considered self-employed when you make money by selling stocks, unless you are doing something such as day trading. Then this income could be considered self-employment income.

 To be engaged in business as a trader in securities, you must meet all of the following conditions:

• You must seek to profit from daily market movements in the prices of securities and not from dividen...
• Your activity must be substantial; and
• You must carry on the activity with continuity and regularity.

Otherwise, selling stocks would be considered investment activity and would be entered on Schedule D.  You should have received a 1099-B from your broker which you will enter by selecting the following:

You would enter the 1099-B by selecting the following:

1. Federal
2. Income
3. Show More next to Investment Income
4. Start next to Stocks, Cryptocurrency, Mutual Funds, Bonds, Other (1099-B) 
5. Walk through the steps to enter your 1099-B   

Note, your navigation sequence may be slightly different.  You can also use the Jump to feature by entering investment sale in the search bar at the top of the screen. 

You said your social security is not taxable.  This is true for some people, but it does depend on your total income.  If your total combined income is over $25,000, then your social security does become taxable at up to 85%.  So if your social security is $25,000 a year and you are profiting $20,000 in stock a year, your social security would be taxable income as 1/2 of your social security plus the $20k would be over $25,000.   

Taxability of Social Security & SSDI

• General Rule: Social Security benefits are not fully taxed. Depending on your "combined income," up to 85% of your benefits may be taxable.
• SSDI Treatment: SSDI (Social Security Disability Insurance) benefits are treated exactly the same as regular Social Security benefits for tax purposes.
• Thresholds for 85% Taxable:
  • Single: Combined income above $34,000.
  • Married Filing Jointly: Combined income above $44,000.
  • Married Filing Separate: Benefits are taxable at 85% regardless of income level.
• Thresholds for 50% Taxable:
  • Single: Combined income between $25,000 and $34,000.
  • Married Filing Jointly: Combined income between $32,000 and $44,000.
• Calculation Formula: "Combined Income" is calculated as your Adjusted Gross Income (AGI) + Nontaxable Interest + 1/2 of your Social Security Benefits.