I used to be tethered using 4.3.5 and I never had to do a tethered boot because I managed my power really well. I used to make sure that it put it on charge every night.
Ok, so you need to take the plunge and upgrade your phone to 5.1.1. Then you need to jailbreak your device using the jailbreak utility Redsn0w. Now I could go through ever step with you here, however i'm going to point you in the direction of a really good tutorial and the guy that does this site explains things really well for first time jail breakers.
Here is the link. Follow this and you will be jail broken in no time. After you have done it, take a tour around the website as it is very good and helpful.
Jailbreak 5.1.1 iOS on iPhone 4,3Gs, iPad, iPod Touch 4,3 Using Redsn0w
Any probs or if you need more advise, just shout me here again.
Good luck