This is tricky. You can claim a partial exclusion of your gain if you moved due to unforeseen circumstances. There are some "safe harbor" rules; if you meet these rules, the IRS will not question the exclusion. The safe harbor rules relate to changing jobs, losing a job, medical reasons, and a couple other things. If you don't meet a safe harbor rule, you can still use the "unforeseen circumstance" rule to claim a partial exclusion, but the IRS may audit you.
The partial exclusion rule means that if you lived there 8 months, you can exclude 8/24th of the normal $250,000 limit. The actual percentage is calculated based on the exact number of days you owned or lived in the home as your main home, whichever is less. For example, if you moved out after 3 months, or 90 days, but you didn't sell until 8 months, your exclusion would be 90/730, or 12.3% of the usual limit, or about $30,000.
Turbotax will calculate the partial exclusion for you, if you tell the program you moved out due to unforeseen circumstances. You don't send proof with your tax return, but keep proof for 3 years in case of audit.
To reduce your capital gains further, be sure to document every possible adjustment. You can increase your cost basis by certain of your closing costs when you bought the home, and you can decrease the selling price by certain expenses of selling. This is all covered here https://www.irs.gov/pub/irs-pdf/p523.pdf
Whatever part of your gain is taxable, will be taxed at regular income tax rates. You did not own the home for more than 1 year, so you don't get the special long term capital gain rate. The rules on the holding period for long term capital gains are still enforced even if you qualify for a partial exclusion due to unforeseen circumstances. Your regular income tax rate is probably 22% or 24%, but could be as high as 37%.
To avoid a penalty for under-paying your taxes, you should make an estimated payment as soon as you can. (For a sale date of April 1, the estimated payment was due June 17.) You can pay at www.irs.gov/payments. Choose "2021 estimated taxes" or "2021 form 1040-ES" from the drop-down menu. Be sure to tell Turbotax about the estimated payment when you prepare your return (Turbotax will not automatically know.)
To report the capital gains you would include a form 8949 and a schedule D on your tax return. Any tax program should do this automatically.
