If I have an aggravated DUI, is that a felony?

In NH, as a general rule, an aggravated DUI is charged as a misdemeanor. However, if there was bodily injury involved (even your own) than it will be charged as a felony. Accordingly, the penalties imposed will vary. Since you gave no details its hard to advice furhter.

As for a lawyer, if you meet income eligibility requirements one will be appointed for you (for either a misdemeanor or felony). However, there are guidelines that must be met. If you do not meet them you will be denied court counsel. In that event, if you can't afford a private attorney, then see if you are eligible for representation by legal Aid (they have different income requirements). Also, contact the County State Bar association to check whether or not they have a list of attorneys who will take case for free/low cost.