Here’s what I see:
-You need to get used to walking forward. HP Rasenha, Sappo, and jumps are all risky options for getting in. No need to overcomplicate the matter. Get as close to your opponent as they’ll let you. It’s also a good test to see how prone your opponent is to pressing buttons.
-Go into Training Mode and learn the distance where s.MK barely misses. This is where Karin wants to set up her offense. From here you can fish for counter hits, dance in and out of your opponent’s attack range, bait whiffs which you can punish, or dash in if you thinking your opponent is sleeping, etc, etc. Obviously, match-ups will determine how long you can stay at this range, but it’s where an opponent has to start being wary of your offensive tools.
-Stop back dashing/continuously walking back into long range. You’re giving up position. (example @ 01:03. Alex whiffs a s.HP and you walk to the other side of the screen. You should have either poked him with one of your longer normals, dashed in to take advantage of his recovery, or if you were afraid he might throw out an EX elbow, stayed put and blocked to see what he was going to do next). Sometimes, you have to give up your position, but your opponent should have to force you there, you shouldn’t be walking back that far for free.
-Stop using c.HK at a distance it can so easily be punished (example @ 01:11). Thankfully, your opponent didn’t know he could get free damage, but against even a slightly better player, you’d be paying dearly. Use c.HK primarily as a whiff punish or as a simple punish against attacks with high recovery (example: when you block someone else’s sweep). Most importantly, learn the distance where c.HK barely tags your opponent. Even at this range, it’s still punishable, but it’s significantly harder to do so.
-Incorporate s.LK, s.LP, c.LP into your game. These normals are +3, +2, +2 on block. They’re key to her frame traps and on CH, they combo into Mediums. In short, they are a huge reason why people are so afraid of Karin when she gets close. I don’t think I saw you use them once the entire set.
TLDR: Walk forward instead of doing risky shit to get in, learn s.MK range and how to mount an offense from that distance, stop using cHK so damn close, and use light attacks more.