Is there a way to change the color of a sink without buying a new sin

if it is porcelain you can paint it with porcelain bath tub paint -- but it won't be 'stainless' might be cheaper to put in new sink and use this one in the garden potting shed area

I see people getting rid of new, or practically new stainless steel sinks often. Keep an eye on Craigslist and Facebook groups, if cost is an issue. I once got a nearly new enamel coast cast iron Kohler since for free because someone bought a house and didn't like the sink that was in it.

Yes. There is a special paint available just for appliances and bathtubs/sinks. If your current sink is metal, a distressed finish looks cool. But as with any old metal... make sure it's not lead first ;)

It sounds like you have a porcelain sink and yes they do have paint for tubs/sinks.

Find a professional that glaze over sink. It will last longer.