If you were to implement as per your original mockup, I'd be concerned that some users will be confused by the choice for the field label.
If you think about it, a field label is a piece of text saying: "you need to provide this information here". Using this principle, multiple field labels (in one drop-down) would suggest to some users that they need to provide answers for all options. But that's actually not what you're after.
Building on what @ltumac said, I think you have:
- 1 field label ("Phone" etc)
- 2 fields (one for the number, one for the type)
I don't see any problem with having these two fields together.
However, I would caution against using @ltumac's toggle link, because this is not a familiar behaviour when it comes to forms. Toggle links usually do something (e.g. expand and collapse), rather than being an answer to a question. Moreover, the toggle link doesn't show the user what the options are, whereas the drop down does.