Where did you get them from? Are they indoor or outdoor?
Being scared doesn't necessarily mean she is younger, animals have different personalities just like humans and some are more timid than others. It also sounds like she doesn't like being picked up either (this is normal) so, as you are picking her up on a daily basis, she may be associating you with this and hence is constantly worried you are going to pick her up when you are near her. I would leave off with the picking up if you can, at least for now whilst she settles in - can she get into her cage by herself, if you tempt her in with food? If not, a ramp would be a good idea so she can come and go from her cage when she likes, as knowing she is able to get back to her 'safe place' if she needs to could help with her confidence - rabbits are prey animals and need to know they have a bolt-hole to run to if threatened.
Here is an article about bonding with your bunny that can help you to gain her trust:
http://flashsplace.webs.com/bondingwithyourbunny.htm
Here is another one all about handling that I found very useful:
http://flashsplace.webs.com/handling.htm
As I said before, being scared doesnt necessarily indicate a younger bun, but being smaller does, although it may be that she was the runt of the litter or perhaps isn't doing as well health-wise. I think taking them to the vet like you suggested is a very good idea, to rule out any health problems that may be stopping her from gaining weight and growing properly.... have you got a pic to show the size difference? Is she just small, or thin too? If she is a bit timid, is she getting her fair share of food or is her sister eating it all?