Could not find an exact answer by reading forums, so here goes....Thanks for your time!

I have a flip-flop hub (on a motobecane phantom cross-uno - pretty good low-end commuter bike imo), with 16T freewheel and 16T fixed on the cog side.
Been invited to do a duathlon (first one so not going to go off and buy a new bike for it). Although the gear ratio I have is fine for commuting, 38-16 - normally I use the freewheel as there are some decent hills, I tend to max out around ~20mph. I thought a cheap way to get a bigger ratio to race a flattish course would be to add a smaller cog on the cog size (14T ?). Here's where my ignorance comes in.

Can I get a 14T freewheel? If so will it be able to go on either side of the hub I have? I know you can put a freewheel on the cog side, but it seems that the only 14T freewheels are BMX and won't go on the hub I have (chime in if this is wrong).
I guess I could put a 14T cog on the fixed side and race fixed, but I'm a wuss and like to coast. Other option is to change the front cog put I'd like to keep the 38-16 ratio for commuting.

Thanks for your help, apologies if there's already a thread that answers this.