I was pregnant with twins and put on bed rest by my doctor. I received state disability. Will I receive a 1099 tax form for that income?

In general and it may be different in your state. But disability doesn't count against you as far as taxes goes. The reason being it is a insurance compensation for loss. Now if you had been laid off and collected unemployment that can count against your taxes as income provided you make over the minimum levels.

Payments you received from a disability insurance policy that you paid the premiums for are not earned income. It does not matter whether you have reached minimum retirement age. If this policy is through your employer, the amount may be shown in box 12 of your Form W-2 with code "J." Then it will be reported as income.