First, the website that is cited is unreliable. The facts to back their claim up are cited as "social media scumbags". No one made COVID-19 in a lab, and nowhere in any source listed does it suggest that. The former head of the CDC also did not sound any alarm about it. The part you are criticizing is where he says, "They don't prevent infection, they do have side effects." This is not new information and most vaccines do not prevent infection they support the body in fighting the infection to limit the damage it can do. This is not sounding any alarm and is simply stating a fact about the vaccine, which is fairly well known.
To discuss your main claim, I found it difficult to find a definitive answer as the topic is highly riddled with misinformation. Some suggest that COVID-19 could have spread due to a lab leak, but to say it was made in a lab with the intention to cause destruction is exaggerated heavily. There are no reliable sources that contain evidence on this claim. Cited is an article explaining where pandemics come from, and one item listed is animal exposure, which is the original claim in the outbreak of COVID-19.
https://www.pfizer.com/news/articles/where_do_pandemics_come_from
Overall, the likelihood of COVID-19 being started in a lab is extremely low, and the rest of the claim is misleading and false.