The best thing an amateur can do in times of crisis is to follow experts, specifically the expert consensus and not the hand-picked cherries who pander to one’s preconceived ideas. Not that the consensus is automatically true, but it probably is the best that human knowledge can offer at the moment. What we are seeing right now is a consensus shift regarding the wear of facemasks, as more and more countries recommend them or even make their wearing mandatory in some places.
This is accompanied by new research, and one such research in the Czech Republic focuses on comparing various materials. The findings are not published yet, but one such preliminary finding is mentioned in the Czech article – five layers of ordinary t-shirt fabric are effective at catching nearly all particles of the size that have droplets exhaled/coughed out. That is huge since it is nearly equivalent to a surgical mask. And since the main argument for widespread use of face masks is that they should slow the spread of disease from those who have it (especially those who might be asymptomatic), then yes, even such self-made masks are better than nothing, if everybody has them.
But the article mentions another thing, which is even more interesting. One layer of t-shirt fabric was able to stop 11% of the much smaller sizes, those that are expected for the dry incoming particles. And five layers would stop nearly 46% of such incoming particles at maximum breathing speed (i.e. during intensive exertion). Slow breathing increases their efficacy.
That might be significant. There is some evidence that the initial viral dose of SARS-CoV-2 might have an influence on the severity of the illness. That seems logical – the illness has several days incubation period during which the virus grows in the body exponentially. A smaller viral dose thus might give the immune system may be a whole day or even more to develop appropriate antibodies, as is the case with influenza. But I could not find any study looking at whether there is a correlation between the incubation period and the severity of the disease.
It is a work in progress, but to me, it seems the answer to the question in the title is “very probably yes, possibly even for your own protection”.
Before you submit any argument against wearing face masks, please consider whether said argument could be used with the same weight against the universal and non-controversial recommendation of washing your hands. For example, an argument that many people are wearing masks incorrectly is not an argument against wearing them, just like the fact that most people wash their hands incorrectly and insufficiently was never an argument against hygiene. It is only an argument for making an effort to educate the public.
Like this video, which educates about both.