I feel my left breast implant has rotated sideways and it feels like it's not centered. Do I have to see a doctor?

If it is simply a matter of asymmetry caused by an implant that has shifted then you have two options - 1. live with it as it is or see a plastic surgeon who can advise you on your options.  If it is causing no problems other than asymmetry then there is certainly no emergency to do anything.  It is simply up to you whether you want to do something about it or not.

Yes, a plastic surgeon will be able to tell if any positional issues or rotation has affected your implant.  Depending on the age of the implant and if any device malfunction has occurred, the surgeon may recommend exchange of your implant vs repositioning.  Best wishes!

If you have some concerns about your breast and playing should always contact your plastic surgeon. If you have an anatomic implant you most definitely need to see your plastic surgeon. A round implant would be difficult to tell if it's rotated since it is round.

If it's bothering you, it makes sense to have it checked. It would be better if you had the implant information. If it's round, then flipping wouldn't be the cause of the appearance change.

An over expanded saline filled breast implant can flip or the capsule can stretch.  Both can causes a malposition of the implant.  The only way to know for sure is to be examined by a plastic surgeon.  

Yes you should see a board certified plastic surgeon for an examination.  Significant change in position of your implant to the side may indicate a tear in the internal capsule surrounding your implant.  It would be unusual late after an implant for this movement take place.  It board certified plastic surgeon should be able to decide if a revision is necessary.