Is it normal to have burning sensation after stitches splitting?

Sounds like you have a small opening that is raw and very sensitive.  That alone is ok and not a problem, however you want to make sure it's not a deep wound and that the underlying breast implant is not exposed because that is a serious problem.

Yes it is normal to have burning sensation after stitches split. Usually if you keep your wound clean the split should stop within a few days and the burning sensation should improve.

Some discomfort in your incision is common, especially if you are spitting sutures.  The advice you were given sounds reasonable.  You should take your temperature and if it is elevated  you should call your surgeon right away.  Otherwise it is reasonable to wait a few days. 

If you have a fever it is essential that you see your surgeon ASAP. Other than that, the recommendations sound appropriate. All the best. 

Yes spitting stitches can be painful.  However it is very important that she see her plastic surgeon as soon as possible to make certain that the suture material is removed and that there is no surrounding infection.  Ask your plastic surgeon if Epsom salts soaks would be helpful.