I have had my hair red for about a year now. It honestly just depends on the shade of red you go. If you are going for a more copper color, I would stay away from like orange-reds. If you are going strawberry blonde, you can most definitely wear a red dress. Dark red would be okay with a red dress. I totally get the struggle though. I have been many different shades of red. I am naturally a strawberry blonde, but I LOVE my red hair. I even had some purple in it. It really just depends on the shade. I tend to wear dark purple, turquoise/green, blue, and olive green a lot. They go beautiful with red hair.
It can look good yeah but generally it's good to have contrast with clothing like black hair with red dress for example the two colors contrast and make each more visible as opposed to red and red but it still looks good just not in the same way.