Yes, it is necessary to report your income and expenses on Form 1040 Schedule C if you are self-employed.
You are being audited for not filing a Schedule C. Your deficiency is the amount of social security and medicare tax the IRS figures you owe.
If your activity is a business, you are required to report your income and expenses on Schedule C, and to pay income tax, social security, and medicare tax on your net profit. If this is the case, prepare an amendment to figure the amount of tax, and then reply to the letter stating the amount you figure you owe. Be prepared to provide documentation of your expenses.
If your activity is a hobby, you are required to report your gross revenue on Line 21 of Form 1040. Your related expenses may be deducted on Schedule A, subject to a 2% of AGI floor and not to exceed your hobby revenue. If your current return is inaccurate, prepare an amendment for your hobby activity and reply to the letter. The burden of proof is on you that you have a hobby, not a business.
In either case, respond timely to the letter or your response may be disregarded.
See IRS Pub 535 for more details on how to determine if you have a hobby or a business. The main criteria for a hobby are that it is not carried out to make money, and you do not expect to make a profit.