I started off just taking L-glutamine before and after my workout and creatine after my workout. I just started taking whey protein and noticed it contains L-glutamine. Should I continue to take the L-glutamine with the Whey that also contains L-glutamine?
Glutamine falls into the lower-tier category of supplements, where it would be extremely difficult for anyone to prove that it's going to make measurable impacts to performance. Glutamine has positive impacts related to DOMS, as an example, but the impact is minor.
Glutamine is an amino acid found in a variety of dietary sources (most meats, eggs, beans, wheat, etc), and as you noted it's also found in whey.
Additionally, it's a non-essential amino acid, meaning your body can generally synthesize whatever it needs from other components. Occasionally your body would be unable to cover its glutamine needs from synthesis, but again you (most likely) get it in your diet already from a variety of sources.
So when you hear people talking about the benefits of glutamine, take all that into account. Anyone who swears up and down about the benefits of glutamine would need to prove that they require the supplementation of it, as they aren't naturally providing enough.
That's mighty hard to prove, anecdotal otherwise, and shows the overall marketing hype related to glutamine.