Is It Okay to Wear Headgear with Invisalign?

If your orthodontist feels that headgear is the best treatment, then you can always try it for a while. If you don't like it, then he can do the elastics, which would probably be more comfortable for you but would lengthen your treatment time.
If you're a stay at home mom, then you are a perfect candidate for the quicker headgear treatment.
Dr Thomas

Headgear can be used with Invisalign. But, it is uncommon to consider headgear use in an adult since its primary use is to modify jaw growth in adolescents. And, since you describe your bite as being asymmetric, and headgears act symmetrically, rubber bands might be a better choice. I recommend having a discussion with your orthodonitst about his/her reasoning in recommending headgear in your particular case. Maybe there are cirumstances, that are not clear in your description, that make it a logical choice. 

From your description your bite sound asymmetric; ie, different on the right than on the left.  In a case like that headgear may not be the best choice since it corrects both sides equally.  This means that it would push your class I side into a class III while correcting your class II side to a class I.  Still, there may be a reason to use headgear so the best course of action would be to ask your orthodontist to explain the situation in more detail.