He was injured too when he used the force to knock Rey up into the tree and KO her for a minute or two.
As you noted, he was further injured by Finn. Which leads to ...
It's a stretch to believe that in all his years training, he never was adept with the lightsaber and it's hard to believe when we see how quickly he dispatches Finn after taking a graze. There is no way Rey should've been able to do what she did with no training, she hadn't even met a Jedi yet. I just don't like perfect and flawless mary sue characters who appear to do everything, Luke was barely able to use the force to move a lightsaber a foot away in the second movie but we have Rey doing mind tricks and going toe to toe with an experienced user of the force.
I think the biggest point to be made is that Ren didn't handily dispatch Finn. He was further injured by that confrontation. Meaning that he really isn't all that skilled with a saber to begin with.
And, still, he
had Rey on the defensive - until she channeled the Force (and became more focused, purposeful, and in the moment than Ren).
So, given everything going on, the confrontation plays out in a very plausible way, IMO.
And yes, one could critique how quickly Rey grows in power and focus with the Force and manages to also be good at piloting and mechanics. But, there may be a valid rationale for it (being Anakin's granddaughter, for one). If it's never explained, I think the criticisms will ultimately be valid.
But until then, I find "Mary Sue" labels to be a lazy form of critique because they oversimplify the characters in question and don't actually focus on details.
She gives me the Wesley Crushers.
Oh well.