I created several backlinks for my website through comment postings. I've done this for about a month now. I know for a fact that several of the comments have been approved because I see traffic from them. However, when I go to Alexa or SEMrush, they don't show any backlinks for my website. Why is that?
Backlinks that you create are not authority backlinks.
Good points. I know what you're getting at. But that's a bit off topic to what the OP is asking.
The question to answer is, why does the backlink not show up in backlink reporting services? The answer is that it's a technical issue related to how often those services crawl the entire web and how often they refresh their data. It could also be a reflection of how complete their crawl is and what kinds of data they choose to report.
You can also look at your backlinks through Google Webmaster Tools, Open Site Explorer, Yandex, aHrefs, and several other sources with pretty big indices.
Martinibuster is correct that you are likely just dealing with the fact that those services don't have the most complete index. Additionally, if the only links you have are the ones you recently built, then you probably don't have enough authority to get any type of prioritization by most of these crawlers.