Hola Matthew

Tener que and Necesitar are pretty interchangeable, but if we are a bit more specific on the more typical scenarios when we use one or the other, we can see some tendencies.

If you are talking about some sort of "need" in a general sense, you can say:

Tengo que ir al médico.

Necesito ir al médico.

However, there is a "tendency" to use necesitar when we are talking about some kind of physical or mental need; for example in:

Necesito beber agua. (I need to drink some water.)

Necesitas dormir un poco. (You need to have some sleep.)

Necesito conocer a gente nueva. Nunca salgo. (I need to meet new people. I never go out.)

But, really, in practice, you can't go wrong using one or the other.

Saludos

Inma