I am sorry to hear you are feeling unwell.
Recovery from sepsis is a long process. Although you were hospitalized for six weeks, your recovery is really just starting. It is not at all surprising to hear that you are sleepy and tired, unable to do household chores and such.
Personally, I found the home recovery period the most frustrating aspect of my entire recovery. While in hospital, I was very sick, but then I really expected to be sick. And I was asleep most of the time so I didn't really care so much; I guess I was too sick to be worried. Plus, they gave me pain medication, so I probably felt better than I was. And there was no nausea from the medication because everything was given via IV. So then I went home on oral antibiotics and really expected to start feeling better - but I did not. Sure, I could walk about the house, but I was good for nothing, exhausted, and nauseated from the medicine. It took me months to begin to feel more normal. Even after I started leaving the house and acting more normally, I was not the same intellectually.
I hope you are staying in touch with your physician. As you can now see, you are really not over this 'little' bump in life. Get the support you need. You may need physical therapy, home care (someone to help you bathe or do housework), or even counseling. Every situation is different. Do not be embarrassed to ask your physician, family, and friends for the help you need.
Just want to warn you: after both of my sepsis episodes (yeah, I went through it twice), I found that my physician was neither terribly cognizant nor sympathetic about post-sepsis life. She said that, now that the sepsis incident was over, I should be fine. Apparently, a lot of physicians think that way; they believe that once the acute attack is over and you've been discharged, everything's OK. But that's not true. Lots of sepsis survivors have experienced this attitude from their post-discharge physicians. So, please stay in contact with your physician and let him or her know exactly how you feel. Your physician can write orders for home health care, therapy, etc., but they won't know what to offer you unless you speak up!
Best wishes for a complete recovery.