hi,
Just by your description of your hair type and problems, i wouldn't recommend hair extentions, as it will strain your hair more, and make things worse.
Do you dye or bleach your hair? As your hair shouldn't be as brittle as you say it is, unless you use a lot of hair products. Also, you many notice a lot more hair falling out when your hair is long, because the strands are long itself. But you do loose naturally about 100 hairs a day, believe it or not!! Could be less or more depending on the person. Its hard to believe because it sounds like a lot, but thats what everyone says. So the loss of your hair when its long could be natural.
There are different types of extentions. There are ones that are knotted with your own hair, glues to your own hair, or glued to your scalp.
The best for you would be the glued to the scap extension. Yet, you should test the glue that they use on your head first, just incase you get a reaction to it, as it will be there for weeks to months on your skin.
But, by the sounds of it, i would fix your natural hair, then work towards extentions. Hair tells a lot about a person, if their healthy or not, so maybe you should get that check out, just to be on the safe side again!!
HOpe that helps!!!
Liz