I second Dr M's opinion based on my own experience and the recommendation of an oral surgeon in my family.
Check out this paper by the American Association of Endodontists:
The adverse effects of overusing and misusing antibiotics are highly publicized in the health professional literature, most recently in the August issue of the Journal of the American Dental Association. According to the Centers for Disease Control and Prevention, more than 2 million people in...
www.aae.org
The radiolucency is a periapical lesion, a secondary infection when the one inside the root is pushing through the apical foramen. This means, the inside of your tooth is infected, too, to a point where the pulp cannot be saved.
Root canal is the minimum, extraction the option.
What I would consider:
1. Did the clinician find the entryway of the bacteria into the root causing the inflammation (crack etc.) and close it? In my case, the root canal did nothing on two teeth...the inflammation did not go away, as the bacterial supply was not interrupted. One tooth was extracted, the other one will have to be extracted. No cavity, no crack discovered despite CBCT scan and X-rays.
2. How long will a root canal generally last? It is not forever. Ask your colleagues and friends for their experience. You will be surprised what you will hear...