Integral already carries the meaning of "very important", so you would not need to have a "so" in front of it. Also, splitting it into two main sentences would carry your idea across better. There are three main ideas you are sharing, "integral to our adult lives", "lack of knowledge is defined as a type of illiteracy" and "which is seen as a limit nowadays". By splitting them up, your reader would get your idea clearly.

Yes, kind of....but (grammar experts please reply) it seems like a run-on sentence. In other words, too lengthy. The end of the sentence also is a bit unclear as to what the “limits” mean. Some may also say you’re unable to start a sentence with ‘besides’ May i suggest separating the sentence into 2? Possibly something like : ‘Including all aforementioned statements, computer use is also very integral in our adult lives. In current times, the lack of such a skill (is/can be) defined as a form of illiteracy. Whatever limitations you want to express should be added with some detail. Limitations to what, for example. Hope this helps!