Of course, my first reactions would be panic, then mourning. I don't think any sane person could escape that. Most insane people would probably feel it, too.
Panic at finding my little sister dead. Panic when no one answered at 911. Panic as I rushed her lifeless body to the hospital, and saw crashed cars and house fires all along the way. Panic when there was no one there to help her. Then the mourning.
That phase would probably take awhile. At least the first half of the day. My next instinct would be determination to survive. Perhaps not everyone would feel that way, but in the more-than-likely scenario that I did not know for certain that everyone world-wide was dead and that I also didn't know what killed the people around me, I would want to live to find this sort of thing out.
I would probably start by looking for other people. Try the internet, first, if I can get it to work. If no luck, try searching my town more exhaustively than just my route to the hospital. If that didn't happen for me, I would probably spend the rest of the first day mouring, then start again tomorrow.
The next day, aquire some basic tools and weapons and get ready for a journey. Probably also bury my sister, or at very least entomb her body somewhere safe. Crazy, I know, but how else do you hold yourself together when the world is falling apart?
A crowbar would be a must, as I will likely be doing a lot of breaking and entering. At minimum a pistol, a rifle, and plenty of ammo would be looted from the police station across the street. I would be expecting to protect myself from both animals and potentially from other armed humans. I wouldn't want to go too crazy, though, because I don't want to be condemned for excessive looting when I finally meet back up with the rest of the world.
I'm not sure what I would bring with me as far as food and clothing, but probalby not much. At this point, I would still be hoping to find civilization out there somewhere. I suppose some sort of pump would be necessary for stealing gas, if the electricity is off. There's a Home Depot down the road. Then, it's in the car and off.
I would go northeast a little ways through the town I grew up in and check my parents' house. I would probably mourn there for a while, too. After that, I might stop by the nearby fire station and steal a fire axe. You never know when something like that could come in handy. Then, I would survey Kansas City. On not finding anything, I would return to my parents house to spend the night and say my goodbyes. The next day, my journey would begin in ernest.
Head south. Visit Joplin, Tulsa, Dallas, Huston. Head west. Go as far as I can each day, taking time to explore each major City. San Antonio, Juarez, Tucson, Pheonix. I'd hit San Diego and the Pacific Ocean before the end of the week.
Panic again. At very least, most of the U.S. and parts of Mexico have been wiped out. But the fact that I've not seen anyone doesn't rule out that society is still out there. Maybe the affected area has been quarenteened. In San Diego, try to find some sort of salilite up-link. Surely, that couldn't be too hard in the home of one of the world's largest naval bases. If it is possible to communicate with the outside world, it will be possible from San Diego. I bet that the base is able to keep running for weeks without outside power. Surely, their equipment will still be operational.
Desperately try to conact the outside world. Fail, fail, and fail again. Finally, it looks like I'm getting through. But the connection is to an empty room. I realize that there is no one out there to be contacted. There may be a few scattered survivors like myself, but civilization has without question been wiped off the map. Panic again.
Visit the beach. Maybe take a destroyer for a joyride. Not sure if that's possible, but I'd probably try. Ponder my own existance and what I wanted to do with my life.
Day 10 thru the rest of forever
After this point, it could go one of several different ways.
If it is in fact possible to take a joyride on a destroyer, that will probably be a big part of my long-term plan. If I pick one that is nuclear and either new or recently re-fueled, I have it for about 20 years before the core runs out. I'm sure I'll damage the thing due to my own ignorance of how to run it, but these buckets of bolts were built to withstand torpedoes and ariel assault. I'm sure I'm not dumb enough to sink it. Stock that baby up with food that won't go bad and see the world. Or, at least, the parts of the world with nice, deep harbors. Eventually I'd have to settle somewhere. But it clearly wouldn't be here! I would prefer somewhere easier for sustainence farming, thank you very much. And even at that, who knows. After I have seen the globe, and know first-hand that I am really the last one left, I might not want to cash in on my full three score and ten. Being old and alone doesn't exactly sound like fun. I might choose to off my self at forty, and then the rest doesn't really matter.
If that level of awesome is not actually possible, which I suspect it wouldn't be, I'd probably start by sewing cyanide capsules into the collars of all my shirts. I can think of hundreds of terrible ways to die. I don't want to experience any of them. Any good university will have cyanide somewhere. Just fill up some caps in a fume hood and you're good to go. Sewn into the collar of your shirt you simply have to move your neck down and bite them. If you're so incapasitated that even that is impossible, death is pretty imminent, anyways.
Then, live life. Survive however long I felt like it. Stockpile honey, corn syrup, seeds, and Everclear. (Or better yet, get unpoisoned 95% ethanol from the same university you get that cyanide from. It comes in two gallon glass containers. Don't confuse it for the poisoned kind, though!) Go somewhere lush and live off the land. There are enough areas in California that you could do that in. It would be hard, but possible. Our ancestors did it for thousands of years. Admittedly, few of them ever did it alone, but I could live and enjoy life as long as I wanted. And when the time came, say goodbye. It would be a good run. Maybe not as good as the one I would have had if humanity had survived, but something to be happy about anyways.
(How is that for thought-out? I've been pondering this for most of the day.)