I have a bacterial infection, can this become blood poisoning?

Yes: Depending where the bacterial infection originates and if allowed to go unchecked --> it can spread to the local tissue, into the blood and even into the bone. You should get a physician evaluate your infection if you are concerned.

Yes: Most bacterial infections don't cause sepsis, but untreated, ignored, or especially potent infections can lead to sepsis, severe sepsis, or septic shock and death. Treat infections seriously.