You'll need to contact the payer and get a replacement 1099-Misc. You need to report the income exactly as it is reported on that form. If you report the income as "other self-employed income", IRS will think you omitted the income reported on the 1099-Misc and send you an adjustment letter.
If you need more time to acquire the replacement form, it would be wise to file an extension now then file your return when you receive the replacement document. Please see the following instructions for filing an extension. https://ttlc.intuit.com/replies/3301811
