Generally the maraje say that it is ok as long as there is no touch or look by the na mahrams. In regards to there being no touch or look by a non mahram during the nose job, it is that the non mahram should not see what is wajib on a woman to cover such as her hair etc. Hence the preliminaries to the action should not be haraam.
As for the act of injecting Botox itself has no problem but it's the preliminaries where the problem is whereby if a male doctor where to carry out the procedure and touch the body of a female. The other side which would have a problem is that Botox is a beautification treatment hence if any make up would be done, it would be visible hence covering it up infront of non mahram would be necessary. Otherwise in the act itself, there is no problem. Similarly no problem if a woman were to carry out the procedure.