Pairing it with the glycolic acid can be too strong so if you want to use them both do it on different days. It'll work on your under eyes only if the shadow is caused by hyperpigmentation, which I doubt it is. It's probably your infraorbital structure under your eyes creating the dark circles you see. You can try concealer or tinted sunscreen to kind of mask it.
I'd also say to continue use of azelaic acid to help with your tan and skin texture if you notice improvement.