Will invisalign for crossbite help make my face look more symmetrical?

Probably not: Invisalign is OK for some tooth movement but in order for orthodontics to really affect your facial shape, orthognathic surgery and multiple specialty involvement is usually necessary for adults. Functional orthodontic appliances can do more in younger kids but they aren't useful much past puberty.

Possibly a little.: You can get some minor change in facial shape with proper treatment planning if you have a functional shift with the crossbite but you shouldn't expect any major changes without orthognathic surgery. It will require a full clinical and radiographic exam by an orthodontist well versed in Invisalign treatment planning to see if any facial change can be achieved.

No: Can't correct skeletal imbalance by just moving teeth. You have to also move boney framework which is outside the parameters of clear aligner therapy. Please see fully qualified Orthodontic Specialist for initial exam(usually free) and appropriate treatment choices. More important than "gadget" is training, experience, and skill of operator.