I'm sorry to hear you are still feeling sick. I am also at 13.5 weeks, and I continue to have all-day sickness too. I have actually begun to feel MORE weak and to throw up MORE since I moved out of my 1st trimester. How is your weight doing? Definitely talk to the Dr as they do have some helpful drugs they can suggest. I have noticed over the past week that I am now only feeling nauseated 50% of the time instead of 95% and that I am at least now enjoying the taste of food (before it was just forcing myself to eat.
One thing that I found was that I could not keep down large amounts of water. It helped me to drink something carbonated (like sprite or gingerale) instead of water b/c for some reason I would not throw that up. I don't know if this will work for you, but it could at least help a little. Also ginger teas were useful for me and super sour candies.
I hope you start feeling better soon, but if you don't - know you aren't alone!
Well, I would seek a Dr. opinion on this. They may want to put you on anti nausea medication because you need to be eating to help that baby grow. Morning sickness normally subsides once you are out of the first trimester, but not for all women...for some women it sticks around for much longer.