Can filler in Nasolabial folds cause a pushing towards the lip and hence cause vertical smokers lines to form?

Lip lines are created over time, it is possible the lines were present before treatment. Perhaps look at before photos and assess if lines are more predominant now than before. If so, you can treat the lines with Botox or superficial filler injections OR have the product dissolved. 

What can often happen when having any procedure for the first time...is that after the procedure you look very, very closely at the region and you find things that you never noticed before. I am not saying that the case here...but its very common in plastic surgery. So much so, that many surgeons will point out specific things about a particular region that may become more apparent after the treatment is performed. Your eyes naturally find other things to focus on, now that your previous focal point has been addressed. We document before and after pictures for every case so it is easy to determine whether or not an area of concern was present pre procedure. If your surgeon took pictures, then that should help determine if he caused the new finding or whether it was present before. Hope this helps.Paul

A common issue I see is that patients don't look at their face critically until after a procedure is done.  Then they are looking in the mirror, often a 5x, and see things that they think are new. That's why we as doctors take so many pictures. To see if things were there before and to note the changes. The unevenness from the filler is correctable. My guess is verticle lip lines were present before. 

I have never seen this occur so cannot say very much.  If you do not like the filler it is easy to remove with enzyme.  Be sure and go to the MD that did your filler and say your concerns.   My Best,  Dr C