Hello, 

I think "She just had a relationship" sounds a bit awkward, and is somewhat ambiguous as to what 'had' really means. "She just got out of a relationship" is better, as this is the colloquial term people use for someone that recently stopping dating someone else. The connotation of her breaking up with the other person is very subtle--the term usually used for that sort of thing is "She just ended her past relationship", or "She just dumped _________". I suppose if you wanted to play it safe and avoid the connotation altogether, you could say "Her last relationship just ended", but to be honest "She just got of a relationship" is the most colloquial phrase that comes to mind for this situation.