Hold, meaning a grasp on something, is a very old word in the language. The OED traces it to 1300, and it is idiomatic with a number of verbs, including catch, get, lay, lose, seize, and take. We may therefore analyze I got hold of Tom's address as
I (Subject)
got (Verb)
hold (DirectObject)
of Tom's address (Prepositional Phrase Complement of hold)
(I've changed your example to show that the simple predicate is got, eliminating the distraction of need+to-infinitive.)
There are two reasons not to consider got hold as a phrasal verb. First, it's understandable from its parts. To get hold is to obtain a grasp. This is quite different from the verb in
I have to look after my brother
which doesn't mean that I have to look past him. Secondly, we can add adjuncts freely between the two words:
I got a definite though tenuous hold on the handle.
We can't generally do this with a phrasal verb:
* I have to look this afternoon after my brother.
The indefinite article may appear, as in the song lyric
You've really got a hold on me
so it might be tempting to think that the phrase started with get ahold, with ahold the (now obsolete) nautical adverb for bringing a ship into the wind to hold her steady. But the OED finds an earlier use for get hold than for ahold (the latter fittingly from The Tempest).