Simple 3D programs do not have photorealistic materials nor rendering. They cannot for ex. handle glass transparency, light refraction nor metallic glosses.
Illustrator's 3D is even more limited. You can have only extruded or revolved shapes, the grooves in the cap of your bottle is unreachable in Illustrator.
If you can accept non-photorealistic shading and limited control on light and camera placements, you can use some entry level CAD program to create the geometry. The rendering result unfortunately will be quite plastic. Placing images on surfaces is the only way to get something else.
The next example has one elementary attempt to make the bottle from scratch in such entry level CAD program. A GDSE screenshot is used as the label. There's 3 differently rotated copies of the same bottle:
The program is DesignSpark Mechanical (Win 64bit). It's free and so simple that one can be productive in days instead of weeks or months. It has SpaceClaim under the hood, but with quite reduced geometry creation options. That's common with free versions of commercial programs. But it's still much more flexible than Illustrator's 3D.
Sometimes there's a need to place a photo of an existing bottle to an image composition. It's tricky but it's surely useful to know something of it, too. Placing a new label is as necessary. See these, if you are interested:
Photoshop: How to make shadow more realistic
How do I wrap a label around a bottle
ADD: You have seemingly already got something. Tilted bottle with horizontal liquid surface in 3D needs the liquid inside the bottle. You have got another answer which shows how well high end 3D modelling can make it. A simpler approach is to insert inside the bottle a transparent solid piece which fills the same space that the liquid would take. To make it seem plausible one must have photorealistic materials and rendering which take optical effects refraction and reflection properly into the account. Here's an example with my simple non-photorealistic CAD program:
The green part is a revolution shape sliced to 2 pieces with a 30 degrees tilted temporary plane. The revolved sketch was the same which was used to make the hollow bottle interior, but scaled to 0,5% bigger size to be sure that there's no random gaps caused by rounding errors when the green part is placed inside the bottle.
In the next image the cap is again visible, the yellow ring is colored to grey, the green fill is placed, the composition is tilted 30 degrees and the bottle body is made 50% transparent:
As you see it's not at all plausible due the lack of photorealistic materials and rendering. Transparency without optical effects doesn't make it glass.