Can someone die from a infected tooth?

I had a root canal done on my teeth about a year ago. Unfortunately it got infected. To the point that the back portion of my tooth broke off. The root canal was in between 2 teeth. The gums is pushing through the teeth as well so I have to get it extracted now.

Was about to when I got pain on another tooth on the other side of my mouth. I went to the dentist on Saturday where they told me the tooth is infected. I have no insurance and little money. The cost to save the tooth was about $3,500. I decided to just pull the tooth for $400. Its all the way in the back so it won’t be noticed. The procedure will be done tomorrow. After that I have to find some money to get the 2 teeth with the root canal extracted as well.

I heard people have died due to an infected tooth. When the bacteria spreads to the brain or lungs or heart. I heard it is very rare, however I am still pretty scared. I am scared the infection has already started spreading. But since my dentist made no mention of it after seeing the xrays I doubt it has.

After I get this tooth extracted I will save up money to get the 2 with the root canal extracted as well. I am planning to borrow some money to get an x ray done on all my teeth just to make sure there is not any more issues. I have been rinsing my mouth recently with salt water and hydrogen peroxide which I heard helps prevent bacteria from spreading. I am in pretty good shape just suffer from a bit of anxiety. Should I be worried? I really don’t want to die due to a tooth infection.