My work computer has the cs6 suite, my personal computer has cs5.5. Can I savedown a photoshop cs6 file and then open it in photoshop cs5.5 in my computer?
Just save. There are no versions to PSD files.
To confirm, I can't work on any files made in photoshop cs6 on my personal computer (cs5)?
No, you CAN. People work between versions all the time.
Just save in CS6, then open the file in CS5.
The only caveat is that some features new to CS6 won't translate exactly in older versions - but 99% of the file will be just fine.