Definitely get on the probiotics, providing you don't have sibo. I'm not sure how hard it is to get tested over there but investigating your digestive health is a good start. I feel like I have unmanaged h pylori which could play a role, on top of my candida.
L-Glutamine is for repairing muscle so maybe you bought it for the gym? Maybe you could could google starting doses and choose what you think, but anywhere between 5g-40g through out the day (3 times a day).
I think the balance with healing them is keeping trauma down to a minimum, and healing the localised and widespread inflammation. I've read some case studies with spontaneous resolve saying one day they just started peeling less and less until it stopped, so I think you may be right