I found an article on selling part of the land attached to a house which says that the sale is taxable. According to that article, you don't get to benefit from the $250k/500k (single/married) exclusion of gains from selling your primary residence.
You need to figure out the basis of the land. You'll have to estimate what fraction the sold land represents relative to the whole, pre-divided land and buildings, at the time of the sale. Then multiply that by the original purchase price. That becomes your basis. You should be able to rely on the property tax assessor's valuation, just for figuring the breakdown between land and buildings. It's probably safe to assume the land you sold is equally valuable, per acre, as the land you kept. So for example if the assessor said: land $100k building $50k, and you sold 25% of the land, that would be 16.6% of the total value.
The taxable income will be the difference between the sale price and the basis. You can add to the basis any costs you incurred to sell the land. Taxes are calculated only on the gain.
If you held the land for longer than one year, it's a long term capital gain, and you'll owe at most 20% of the gain in taxes. Otherwise, it's taxed at your ordinary income tax rate.
You will need to file an amended return. The "penalty" is more like an interest rate. It's only 0.5% per month, or 6% per year. And it's capped at 25%, a little over four years' worth.
The IRS will only accept amended returns until the latest of: three years after the the tax return due date, three years after you filed your return (e.g. if you got an extension and then filed in July), or two years after the date you paid the taxes due (e.g. if you requested a payment plan). Since you received the payment in tax year 2015, that return was due April 18th 2016, and you do still have time to amend it.
If the unreported income was more than 25% of your reported income that year, the IRS has six years (twice the normal three years) to audit your return. And the state will have sent a copy of the 1099 to the IRS, so they know about it and will be expecting your amended return. Unfortunately, even though the IRS has three extra years to audit you, you don't get extra time to amend the return.
In the future, remember that all money received or paid on your behalf is income unless excluded otherwise.