Upload & Sell: On
I think for the image size you are displaying here, your modifications in general are not bad. If I just saw the after image, I probably wouldn't immediately assume a massive retouch. Considering the extensive modifications you did - in particular playing around with liquify edits - it looks impressively believable to me.
In terms of weaknesses, I think you could have retained a little more skin texture but it is a hard thing to judge at this size online. Her ear looks a little odd where you cloned out the fly-away hairs. I think you dampened the highlights on the face a little too much and it is somewhat inconsistent with the shininess that remains around her chin.
Whether these edits will hold up for a 16x20 enlargement for the wall of the clinic is a whole different ballgame.
Regarding your question about removing shiny highlights, there are several methods but I usually use the healing brush in darken mode on a new layer. Then I either use Edit>Fade or just reduce the opacity of the new layer. The healing brush allows you to copy texture from a nearby area and yet darken the shine.
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Now with that out of the way, I think it would be helpful if you could explain your objective here a little more. My assumption is that these shots are probably for display at a vet clinic or for advertising more than shots for the subjects.
I mention this because if this portrait was for the subject, I think you probably went too far. You crossed the line from flattering retouch to pretty heavy digital make-up. If for the subject, you run the risk of insulting her unless she specifically requested this type of modification. Even if this is technically for the clinic, everyone there including her is going to be able to compare your portrait against reality on a daily basis.
If the objective was to show real people at the clinic, I wouldn't have used liquify at all. I might have squeezed the entire image by 5-10% and used dodging and burning to slim her face a little. Unless she normally wears make-up (and she apparently doesn't), I would have kept more facial texture, including the dark spots at reduced contrast.
If the clinic wanted real people but as gorgeous as possible, I would suggest hiring a make-up artist and hair stylist.
If the clinic wanted gorgeous models for advertising, I would suggest hiring gorgeous models.
I also suggest that you use this retouching work you are doing as a great lesson for thinking about your lighting strategies. As an example, see how you lit up her right cheek? That widened her face by probably 10-20%. See how the left of her neck is lit? That helped emphasize a double-chin.
Posing comes into play, too. Having her lean slightly forward and push her head slightly out towards the camera would have helped quite a bit with the chin and might have helped with the face/body proportions as well.