Voluma is a very thick, structural product that is more suited for deep placement on the bone for cheeks, jawline, and chin. It is not a product to be used for superficial lip lines. For that area, I would chose Belotero or Volbella because they are much thinner and will integrate with your tissue better. However, even when choosing Belotero or Volbella, I must prefer the combination of heavy microneedling with PRP x3 treatments to reduce the lines and Botox to maintain the results and prevent further lines. A final option would be to place a thinner filler like Volbella or Vollure into the lip/lip border itself to provide structure. This does not completely erase the lines, but definitely softens them.
Volbella is a very fine filler that is mostly used for lip border definition and hydration to the lips. It really does not provide much plumping factor. If you're looking to add a slight bit more definition to the border of the lips, then Volbella could be a good option. However, if you are looking to add a bit more plump, then I would not recommend it, as you likely will not see the change you're looking for. I would ask your injector if they split syringes and do a half syringe of Vollure, or, as you stated, find another place in the face to put the remaining product.
If dosed appropriately, Botox should last 3-4 months, sometimes slightly less in the forehead. If it is not lasting that long, you are likely being underdosed. There has been some studies that have suggested that too small of dosage done more often can lead to antibody formation (resistance). But yes, the quoted time is usually from time of injection.