When you say "track bike" are you talking something specifically to take on a velodrome? Or are you just referring to a fixed gear bike in general?

If you're looking for a fixed gear bike for street riding, you can get a lot of bike for $1500. The wabi special comes to mind right off the bat.

For true track bikes I guess the answer depends on the type of track bike you're looking for, NJS steel? Aluminum? Carbon? Are you riding for fun or racing?
As for big bike brands, Fuji made a mid range track bike called the track pro at least as recently as 2018 that's within your budget. Cannondale has the CAAD10 track. Giant makes one called the Omnium.
Dolan makes a nice line of track bikes that I've heard good things about.
This isnt really my area so Ill let somebody else take it from there.