No, for a complex of reasons.
From a technical standpoint with logical formalists, a fallacy must be an inference. The statement you have presented here is, strictly speaking, a proposition and is specifically an example of material implication sometimes called the conditional. Generally, an argument is taken to be at least one explicit premise and conclusion.
But let's see if we can break it apart and find an enthymeme which in modern parlance refers to an implicit proposition that often occurs in the use of natural language and informal logic.
"If you are against criticizing the media, then you are against free speech".
P1. You are against criticizing the media.
P2. (Criticizing the media is a form of speech.)
C. Therefore, you are against free speech.
For this to be begging the question, the premises provided (implicit or explicit), would have to contain the conclusion. Is that the case? Let's ask some questions. Is being against 'criticizing the media' the same thing as being against 'free speech', and if not, what is the relation? One can be against sexual assault and against the Oxford comma, but to claim they were the same idea would be an obvious false equivalence in almost any context I can think of (grammar Nazi's notwithstanding). Obviously the parallel predication doesn't imply identical objects.
But what is then the relationship of the predicate objects? Let's do our homework. The communication media are essentially:
Media is the communication outlets or tools used to store and deliver information or data.1 The term refers to components of the mass media communications industry, such as print media, publishing, the news media, photography, cinema, broadcasting (radio and television), and advertising.3
and free speech:
Freedom of speech2 is a principle that supports the freedom of an individual or a community to articulate their opinions and ideas without fear of retaliation, censorship, or legal sanction. The term "freedom of expression" is sometimes used synonymously but includes any act of seeking, receiving, and imparting information or ideas, regardless of the medium used.
So, the 'media' in your proposition are corporations that communicate using various physical media, whereas 'free speech' is a principle about how media should be used to communicate among individuals in a society. I'm tempted to see this as a difference as a classical separation of policy and mechanism.
Thus, they're related, but not remotely an equivalence conceptually. That should be enough to reject the charge you are begging the question, but let's drive home the point.
Is it possible for media corporations to not honor free speech? Absolutely. China's state-run media outlet CGTN might be used as an example. According to the source:
According to Foreign Policy, CGTN is a part of a global $6.6 billion media expansion campaign involving TV, radio, and newspapers that started in 2009 during the presidency of Hu Jintao, Xi’s predecessor. The purpose of this is to serve as a global mouthpiece for the Chinese Communist Party.
So, would 'criticizing' CGTN among other biased outlets such as RT and Fox News be an act that goes 'against free speech'? Hogwash. In fact, NOT criticizing any communication medium that does NOT honor the principles of free speech might ethically be seen as an act of negligence in regards to defending free speech.
Given my experience, many inexperienced debaters are quick to claim their opponents' arguments are fallacies because they believe it successfully refutes their opponents' conclusions, which itself is a fallacy known as the fallacy fallacy. It's easier and more persuasive to the unitiated to dismiss an argument as a fallacy and conclude the conclusion is wrong, then it is to tease apart the intricacies and explain the contradictions and fallacies that inhere to it.