Hola Paul,

Tengo que and necesito are pretty much interchangeable. When using tengo que we focus more on the "obligation" to do something and when using "necesito" more on the "need" to do something. 

I could say:

Tengo que trabajar. 

This implies the obligation to work.

or

Necesito trabajar. 

I need to work.

This implies the need to do it, because if you don't, you won't earn money and you won't be able to pay the rent etc. So someone with this in mind would probably use "necesito" instead of "tengo que".

I would add that "tengo que" is more commonly used than "necesito", as the latter sounds a bit more formal.

Saludos

Inma