You can practice alone to some extent, but will never be as good as you could be by practicing with peers or coaches. Just like learning a lesson by just reading it vs. learning a lesson & testing yourself on mock exams, doing cases "on your own" will have limited value and poor retention.
If that is really what you want, so suggestions:
1. Read books (NOT "Case In Point", which I think net detrimental; Victor Cheng's book is good however)
2. Speaking about Victor Cheng, use his following resources:
2a. 6 hours of free video on YouTube
2b. "Look Over My Shoulder" (LOMS). Yes there are some free (illegal) versions everywhere, but please honor his work and pay for the product, it is not that expensive
2c. Do plenty of quick math exercises on caseinterviewmath.com, where he will rank you against fellow candidates on both accuracy and speed (in that order)
3. Plenty of great resources are available on the web and obviously here at PrepLounge
Again, none of this will replace actual practice with fellow candidates, and I strongly suggest you work with a coach or current consultant at some point. Many of us have spent over 100 hours to prepare for these cases, you shoul expect to spend even more if you want to work on your own.
Honestly though... if you are "stressed out" when doing a case with a stranger, don't expect to feel good when doing an actual interview. I'll be blunt: I don't think you can get in with that approach. Good luck - but remember it is a competition and the other guys get prepped properly -> you are helping them by "preparing" alone.