Do you need a different harmonica for songs in different keys?
Sure. And this is one of the first things you need to get under control. 90% of blues harmonica is played in what's called "cross harp" or "second position." (Google "cross harp" and you'll find a wealth of information.) Basically this means that you focus your playing on the draw notes of the bottom half of a 10-hole diatonic harmonica; the draw notes are stronger, have more soulful tone, and, most importantly, can be "bent"--meaning that you can lower the pitch of the notes by changing the shape of your mouth. This lets you produce the blues scale fairly easily. But it also means that you have to get used to the idea of playing a harmonica in a key other than the key stamped on its coverplate.
Here's a basic cross-harp chart covering the most common blues keys. MEMORIZE IT. Let me repeat that: MEMORIZE IT. It is the most important bit of rote learning that you--a blues harmonica student--will ever do:

key of song harp key

E - - - - - - - - - - - - - A
F - - - - - - - - - - - - -B-FLAT
G - - - - - - - - - - - - -C
A - - - - - - - - - - - - - D
B - - - - - - - - - - - - - - E
C - - - - - - - - - - - - - - F
D - - - - - - - - - - - - - - G