I used to rip a lot like that. Fairly big, and deep, and almost every practice. I'm level 5 and practice twice a week (like you) so i didn't know if i should have gotten
grips either. For a while i filed my hands where the skin was pealing off between every turn on bars. That worked well for a while and reduced the amount i ripped quit a bit.
Another girl I train with had
grips that she never used so she let me use them. Ever since I have started using the grips I don't rip at all and get to train bars so much more! I used to hate bars because i always ripped and got hardly any practice time, but now i love it!
...Considering my bar routine isn't all that complex (hah) it didn't take me long to get used to them.
Basically, I would suggest getting grips, or at least trying them to see if you like them.
I'm not a grips expert but mine are just like the cloth kind and not the dowel (??) ones...and they are working really well for me.
Two of the other girls I train with just wear grips during practice when they are working on bars for longer than usual, and not during competition, so you could even do that if you want.
(though i think ill wear mine during competition...and will be buying my own asap.)
I don't know if that was helpful but good luck..and i hope your rip heals fast!!