What, you think that just vanishes after the first second or two? "Killed my dad? So 3 minutes ago, I'm over that."
The visual indication is best shown in his acting where he's talking to Rey. He's basically pleading her to join him, for that validation I mentioned earlier. He needs to be right about this. Meanwhile, those words lead Rey to her own self actualization, that she is strong in the force, finally embracing her identity, and overpowers him via that self empowerment.
The visual indications are there, they're just in the acting, not crippled fighting style. Look at Ren's anguished faced, how he's barely holding himself together, beating on his chest. He's trying to convince himself that he's strong now, that the wounds don't bother him, that he can take anything. He killed his father for power he thought he'd get, so he's trying to act the part of the invulnerable, but he's simply not okay, physically or emotionally. The same way that Vader isn't as strong as he ever was in the RotJ with Luke, but Luke's constant "You can still do right by me" meant he doubted himself and was weaker than in their ESB fight.
It's not about the moves. It's about understanding the mental framework of the characters. And people can grin and bare their teeth through pain. THe fact that he is intent on ignoring his injuries and even beating them worse, as if to make the point that they don't hinder him does not mean they're not hindering him.