Afterwards I saw that I got the hard shadow under my chin, should I have lowered the position of the strobes to have gotten rid of this?
I guess it's a matter of taste if there are no rules against it.
Lowering the light gets risky. There is nothing worse than under lighting. We tend to prefer light coming from above.
You could bring in a white reflector to fill the shadow. Since its a tight shot, the subject could hold it.