Just had battery and alternator replaced.
Drove home from store and noticed a loud clicking sound under front of hood. Continued getting louder and faster until I turned engine off. Could it have to do with serpentine belt?

 

Most likely since they had it off replacing the alternator.
Take it back to them immediately.

 

Found out the clicking noise is from my radiator fan. It only gets noisy after driving a while. I was told I need to replace the electric radiator fan motor. Any suggestions on brands, etc.?

 

This sounds suspicious. Did you hear this sound before installing the new alternator? The garage that installed the alternator, either damaged the fan accidentally or sabotaged it just to get you back for more money. Could be a very simple [U]fix.[U] They may just be milking you for easy money. Have someone you trust check out the fan. At the very least spin it by hand (engine off, key out of the switch when the engine is cold) to see if there is a "clicking"noise. I wouldn't replace anything until I was sure what if anything is broken.