The 1.572 million is the gross amount that you received. The net amount will be that gross amount minus the amount that you paid for the stock. That net amount is the amount that you will owe between 10 and 15% on for your federal return and 5% on for your Illinois return.
Since this is a one-off you should go ahead and do the return yourself just like you always do. Once you've finished - if you don't feel confident in the results - you can always have a professional review it before you submit it or re-do the return.
You may get a letter from the social security administration about your benefits. After all, they don't know it's a one time thing. You may have to submit something in writing to them. Watch your mail for a letter.
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