Warping should do the job. Rotate at first the bottle to vertical. It must stand straight.
Place the label on the bottle as a new layer (=layer 1). Let it be about 1,5 times as wide as the bottle. Select the label and goto Edit > Transform > Warp > Custom. You get a grid that you can tweak until it fits. I said "1,5 times as wide as the bottle" That's because then you can move at first the right and the left edge and get quite plausible horizontal shortening at the edges:
Matching the light is difficult if your bottle is blue and the label is white. I guess the bottle is made of white plastics. Adjust next the color of the bottle. Desaturate fades all color. I tried white balancing. It's not especially good choice here, because it easily generates yellow to non-blue areas.
Then select the placed label (=Ctrl+Click the image icon in the layers panel). Use that selection to make a label sized copy of the bottle surface to a new top layer (=layer 2):
Give to the new top layer blending mode=Hard light. reduce it's brightness and contrast with curves as shown for plausible shading. That's taken from the original bottle, but it must be squeezed to keep the paper visible. If you use blending mode = multiply, the paper vanishes. Reducing opacity helps, but I see this method gives more control.
The result is not mathematically exact, but it can be acceptable and doesn't need 3D.
3D needs a 3D model of your bottle. That's not impossible in proper 3D software, but Illustrator's 3D revolve cannot make the neck right.
Of course you can try to make a fake bottle as 3D revolution and place the label perfectly in Illustrator. Then you would take only the deformed label and paste it onto your photo. That's fine in theory, but in practice it's tricky to set the viewing direction and perspective right in Illustrator. Otherwise the the deformed label will not fit. This is an example of fake bottle. The revolved profile is only a guess, it's not based on proper measurements nor math:
Also the label has only screen resolution. It must be a high resolution image or a vector drawing to stay sharp as 3D surface image.
The job would be easier if you had the bottle photographed with long focal length lens from so far away that there's no substantial perspective, only a parallel projection (=the cap top and the bottom are as much elliptical, preferably a straight side view)