Although you didn't quite ask it this way, I see two parts to your question, and I will offer answers accordingly: "Is it okay to discuss personal experiences or observations in academic writing?" and "Is there any difference when it comes to literature reviews?"
Is it okay to discuss personal experiences or observations in academic writing?
Although it is controversial (some people will tell you never to include personal experiences), I think there is a place for personal experiences. But first, you need to understand why this is generally frowned on.
Everyone has personal experiences and everyone has different ways to interpret them. Anyone can write a magazine or blog article sharing their personal experiences. That's just their opinion, which the reader could take as good or bad. What separates an academic article from such opinions is that academic writing is usually expected to be fairly objective (tries to take a disinterested third-party perspective) and critical (takes nothing at face value, but tries to dig under the surface to understand what is really going on from multiple non-obvious perspectives). (One notable exception to this is critical social theory, which does not necessarily try to be objective, but nonetheless strongly emphasizes being critical.)
So, where do personal experiences fit in here? Most of the time, they are not objective (by definition) and all too often, they are insufficiently critical. This is why they are often frowned on. However, I believe they could be helpful and acceptable if the writer considers their own personal experiences this way: "What makes my personal experience more outstanding than other random personal experiences related to this phenomenon?" If there is nothing particularly outstanding about it (e.g. it merely serves to illustrate the point, as do other people's experiences), then it is best not to mention it, since such a mention would weaken an otherwise strong academic argument. But if it is unique or original (e.g., the entire study is propelled by the fact that the writer's personal experiences contradict the dominant scholarly discourse), then it is definitely worth mentioning. However, in such cases, the writer should try to describe their experience as objectively as possible and should be critical in not accepting their own interpretations of their experience at face value. When presented properly, such personal experiences can strengthen the credibility of the writer.
Is there any difference when it comes to literature reviews?
I believe the principle I laid out for academic writing in general also applies to literature reviews. However, there are two levels or two aspects to a literature review that you need to distinguish in this case:
Including your personal experiences as part of the "literature" being reviewed: NO. Your personal experiences are not "literature". "Literature" means published works (by "published" I include grey literature such as working papers; I also include non-scholarly practitioner publications). It does not include unpublished, unwritten anecdotes. That is at best to be considered primary research, which is never part of "literature" being reviewed in a literature review. (Don't misunderstand me; you are certainly free to supplement a literature review with original primary research if you want to, but you just have to clearly distinguish that from the "review" part of the article or chapter.)
Including your personal experiences as part of the introduction or discussion of your literature review: In this case, since you are clearly not presenting your own experiences as part of the "literature" being reviewed, then my comments above apply. I see no problem with this if it is done properly. But again, this is controversial; "controversial" means that your supervisor or journal editor might disagree, and so you might have to drop it regardless.