Do not get this area injected. There are muscles here that affect your smile especially at the sides. Also if you have lax skin, your eyes could just sink open a little and make things worse. Fractionated carbon dioxide laser is the best preventative treatment in my opinion
You probably received strong topical steroids which are inappropriate for long term use, especially around the eyes. The best thing to do is to either nothing or if tolerated, use a lactic acid cream as long as it is not irritating. That would address lightening the area and building collagen and elastin back. Unfortunately, the damage can be permanent so nothing is guaranteed to help.
It's hard to tell what is best from the photo since you are turned sideways, but either wrinkle fillers alone or if you can afford it, fractionated carbon dioxide laser resurfacing and fillers would be best.
Fleshy moles lend themselves well to shave removal. Make sure your dermatologist or surgeon sends the lesion for pathology to be evaluated by a competent pathologist. Lasers in this case would just be a heat source and cause unnecessary thermal damage and risk of scarring (or just need for repetitive treatments). Most importantly, the lesion would not be evalutated for pathology and many "fleshy moles" can actually be skin cancers
Mohs surgery in coordination with sentinel lymph node biopsy with a head and neck surgeon would be a good way of assuring the best treatment for margin control and evaluating the lymph nodes. We often work together for cases like this.
