you're young, you'll be fine.
Having toured and rando'd a bit fixed (in mostly-flat Britain though) I would give you some advice:
Do not leg brake. your knees will quit before you want to...
lower your gearing. plan to go slow and steady. You will have one optimal speed for the cadence you like- you can calculate this. Shoot for 10-12 mph I'd guess.... 40-16 might be good, I dunno, you know better than I do what is comfortable. But plan for lower than usual gearing on account of the load.
Slow and steady is the name of the game. fixed distance rides are actually really nice because they force you to go evenly the whole time. Don't try to push it.
light as you can.... this is even more important on fixed hills...
stretch well, and do some knee-strengthening stuff like sitting on a chair and lifting your legs...
The fixed-wheel bit is actually much less of a problem than the track bike geometry bit. If you can hang your wheels etc on a road frame you will be much happier... just a thought, in case you know someone to trade with for the holidays or something
Id go with actual bullhorns over drops or flat bars. The drops will be too dropped to be useful anyway, and the bullhorns will help you stretch out. I like profile airwing type ones not necesariily that brand, just that shape...
on that note, borrow a riser dirt drop style or technomic stem if you can. Try to lift the cockpit
anyway, thats my advice take it or leave it. sounds fun (kinda) and im jealous (sorta)