A "rough" day is one in which you have a lot of problems, or feel tired and stressed. People especially talk about having a "rough day" at work:
A: Rough day?
B: Yeah, my boss yelled at me for something that wasn't even my fault.
If you want to talk about more than one day, you don't say "rough days". You say "a rough few days" or "a rough couple of days":
Sorry I didn't call you back earlier. I've had a rough couple of days.
The word "rough" can mean "difficult" or "filled with problems" in some situations. Here are some things that people often describe as "rough":
(a company) is going through a rough period
(someone) is going through a rough time
we got off to a rough start