Yes, F is not a super common key, at least in rock. The most common keys in rock are probably E, A, G, and D, but that is specific to rock. In folk, you should get more G, C, and probably F. Jazz will have more flatted keys, typically because of the horns involved. (The “base” key of brass instruments is often not C, but Bb or Eb.)
Now, the key of the harp does not necessarily dictate the music you will be playing in it. “Thunder Road,” as I am hearing the harmonica part in my head, is played in “straight harp,” so the key the song is in should be the key you want your harmonica in. Most blues and rock harmonic is played in a style known as “cross harp” or “second position.” This is where the key of the harp is a fourth higher than the song is. So, a bluesy number in E would be played with an A harp. A blues-rock tune in G would want a C harp.
So your C harmonica should be plenty useful in rocking/bluesy numbers in the key of G. I’m sure a good number of Rolling Stones songs would qualify. “Honky Tonk Woman” comes to mind. Oh, and I do believe George Thoroughgood’s “Bad to the Bone” is in G, so you’d want a C harp for that. And your F harmonica would be good for key of C blues/blues-based songs.
There is too much to cover here, so I would suggest starting with learning about either straight harp or cross harp. I started learning cross harp because I found most straight harp kind of boring, and I wanted that down-home bluesy sound, rather than the more folksy sound of the straight harp. But you do need to read up on those two styles/positions and learn how to use them.
One very basic thing is that in straight harp, you are playing more blow notes, while in cross harp, you are playing your draw notes more. On a C harp, for instance, playing any of the blow notes gives you notes from the C chord. When you are playing cross harp, the first four draws are all notes from the G chord (and if you add 5 draw, you get G7, a typical blues chord.)
What is your level of musical knowledge? I can get more into it, but it’d be easier if I knew what vocabulary I could use. And just ask individual questions. I’m not sure I could write up a cohesive beginner’s narrative on how to play the harmonica, but I could address specific questions better. I’m not an expert, but I do play basic straight and second position harp (with occasional forays out to other positions.) Technically, you can play a diatonic harp in any key you want, but that’s very advanced technique, and only relatively recently has it become popular. Typically, you’ll find most pop harp in 1st, 2nd, or 3rd position.