Is blue color normal for bruising post lip injections, or is it something serious? (photos)

Your lips appear very full.
It may be that the filler was placed too superficially.
Go see the practitioner again for reassurance or resolution.

It would be helpful to know how long ago you were injected and how much product was placed along with any other possible side effects you may be experiencing.  You should be evaluated as your lips do look full/swollen and perhaps a steroid or other modalities may be indicated.  This may be bruising but may also be what is known as the Tyndall effect. 

Sometimes what can happen with filler is that if you have been receiving filler over a period of time, the filler will move more superficially to the top creating a "tindel" effect which causes a "bluish-gray" color.  It's not harmful but is noticeable more to you than anyone else.  This is more caused by hyaluronic acid fillers such as Juvederm and Restylane.  It can be resolved with an enzyme that is injected called hyaluronidase that dissoles the filler.  However, the best thing to do is to consult with your injector.