This may vary from state to state. But, in general, you will need a SR-22 if you failed to comply with your state's financial responsibility law at the time of your dwi. Now, there is really no such thing as "full coverage." Most people use this term to refer to physical damage coverage. Physical damage coverage consists of collision and comprehensive coverage. (Generally, collision insurance covers damage to your automobile caused by collision with another object or by upset. Comprehensive insurance covers damage to your automobile from vandalism, theft or glass breakage. And, most lienholders require physical damage coverage if you are financing or leasing your vehicle.) Chances are your state will be looking to see if you were covered for certain limits of bodily injury liability and property damage liability at the time of your dwi. Now, I assume you are talking about a "hardship" or "right to work" license when you mention an "essential needs" license. Again, this may vary from state to state. But, in general, if you need a "hardship" license, you will need a SR-22. You can follow this link to your state's Department of Insurance to learn their rules and regulations.