@bcraig:
All of the advice offered is good and should be followed up–check her health, talk to the breeder, get a trainer's opinion.
I will say that we have pretty much taken it for granted that Ella does not like to be picked up and in most cases we simply find a way to avoid it. She has never bitten us, but she will growl and her whole demeanor changes and it is obvious it is because she does not like to be physically forced to do something she does not want to do. And that is exactly what picking up a small dog is. Given what everybody says about Basenji independence and not physically bullying your Basenji, I never thought it was an unreasonable request by Ella. And you say that scolding makes it worse. I think most people on this forum will tell you that is typical Basenji bahvoir. They just do not respond well to punishment. You have to be a bit more patient and creative with a Basenji. I know you might feel like you have to stand your ground to show dominance but think about why you have to pick her up and figure out another way to accomplish what you want. That is the sign of true leader. For us, the use treats and toys and commands usually keeps us all happy.
All that being said, Ella let's us pick her up to get into the car (which for some reason she does not like to jump into) and she seems to understand when some rare unexpected emergency comes up that it is OK.
Personally, and I really do mean for ME…it is important that I be able to pick up my dog, and move my dog...because things happen in life, ya know? But it isn't too hard to desensitize dogs to being moved around, even Basenjis...you just change their association from 'person coming...going to make me do something' to 'person coming....going to do something to get a treat' It takes time, and effort...but not a whole lot of skill, once somebody shows the student the timing aspect