It does take time to master the art of getting rid of fill lines.It takes lots of practice and patience.Try to make sure you get rid of any white lines that are still showing.
Make sure you are filing under the line and keep going until it all disappears.Do NOT apply any acrylic until all lines and lifting have gone completely, if you rush things and go onto apply your acrylic before getting rid of those lines you will see them through your finished nail.
The tutorials on here are smashing.I had exactly the same problems as you and I kept at it,then one day it all fell into place and now I am finally happy that I have no nasty fill lines.HTH