Your sink is porcelain over steel (hence the rust). Yes you can "fix" it with epoxy, etc., but it's NOT the same. With epoxy, you must be careful... cleaners, pots 'n pans, knives... whatever, are going to affect that repair.
I only know of one business that will re-porcelain a sink (there maybe others!). It's not cheap... Gigi's Hollydale Appliance & Reporcelain
IMHO, I'd "fix" it the best I could, make a sink cover (so know one knows what's underneath)... then go camping and make MEMORIES! YMMV