First off, most routines are not created for one person specifically, so they won't address that person's specific needs, prior injuries, disbalances etc. So some adjustments will most likely have to be made by each individual person to suit their needs.
In your case, your shoulder takes probably more time to regenerate than the creator of your routine anticipated. Switching your back-day with your shoulder-day might very well solve that problem, giving your shoulder more time before it is used again. It might also introduce new problems, though, as split-programming is a very complex issue.
Depending on the exercises you do, you might introduce other problems, since most exercises use more than one muscle group. Some examples:
- If you're doing the Overhead Press for shoulders, your performance may go down as your triceps might still be sore from the day before.
- Putting back-day after biceps-day might also impede your performance on heavy Pull-Ups, should you do those.
The above are just two examples for your specific case. Depending on your individual genetics and your regeneration of certain muscles, you might not even experience those. Make sure to check your performance on all your exercises to make sure you're not overlooking anything, and adjust accordingly.