I am not a big fan of radiesse. the hyaluronic acids give you more flexibility for the reason that you stated. If you do not like it , it can be dissolved. I do not inject Botox around the nasolabial folds. Botox can be used for fine lines around mouth and of course on the foerhead/crow's feet, glabella, platysma, and chin/jaw line.
The ONLY reason to inject Botox around the nose is to weaken the muscles that lift the upper lip when one has a real "Gummy Smile". Injecting Botox in you would result in further drooping of the upper lip and hiding the upper teeth when you smile.
I looked at you close up picture and I cannot see the "Mongolian Look" you refer to. It is possible that the quality of the picture is not properly rendered on the screen. If it truly bothers you and you do not want to wait for it to dissolve, ask you injector to dissolve it with Hyaluronidase.
BOTOX with Juvederm for lines
In my opinion, the use of BOTOX in the area around your nose would not make the improvements that you desire. It may even create problems. Filler injections should be injected into creases and depressions to soften them.
Botox does not fill lines it act on the muscles that cause the lines.
Your nasolabial fold will not improve with Botox.
Your problem now is filler problem, fortunately Juvuderm can be disolved with Hyaluronidase. That is what you need now to resolve the problem then you can decide what you want. Radiesse stays longer and can not be disolved.
Botox is not a filler and it cannot create volume. It relaxes the muscles that cause dynamic wrinkles or movement lines. Caution and knowledge must be used when injecting around to mouth in order to avoid unnecessary laxity.
Improving the hills and valley of a filler effect on smile folds
Before you undergo another procedure such as Radiesse filling in the face, you should improve the appearance that bothers you, otherwise the next treatment won't provide you with the good result it normally does. I would consider dissolving the Juvederm with hyaluronidase if the placement were truly not ideal. It may be that you need more volume for support but that could only be evaluated by examining you. I would avoid botox injections around the nose as you were inquiring because that could give you an unequal droopy lip.
Botox does not help around the nose
If you want to lift the nasolabial grooves open then radiesse into the cheeks will do that. Botox around the nose can cause changes in smile and is not well tolerated. It also does not have a lifting effect other than in the eyebrow area when done properly.
Botox is not going to treat your nasolabial fold
If you think that your NL folds appear deeper after Juvederm treatment, the solution is not to inject them with Botox. The NL fold is a normal anatomic landmark that is accentuated when soft tissue is augmented along the cheek- either with aging or with misplaced fillers. The Juvederm should have been injected directly into the NL folds. Fortunately, the fillers are temporary, and should disappear in a few months. You can ask your doc to dissolve the filler with Hyaluronidase if you dislike the look the treatment has given you.