Sorry if I am about to reiterate some things already said.
But really, it depends on how much you fingerspell, how you do it, what other activities you do, and if you have any other existing conditions.
You also say you avoid it, this may be a factor in itself.
However, some fatigue is normal. Especially if you are not used to the activity. Fatigue is not necessarily a negative symptom... it depends on why you are getting it and how severe it is, and if it is actually causing pain.
I often feel fatigue and stiffness in my fingers and forearms (from typing, fingerspelling, etc). Some of this is normal (muscles tire with use).
Though RSI (e.g. carpal tunnel) is usually triggered by excessive use without rest or change, coupled with improper techniques which put a strain on muscles, ligaments and tendons.
Tendons and or ligaments can rub against each other, or be strained, they become inflamed and raw which makes them more prone to this rubbing irritation, and it continues on in a vicious cycle. Joints usually wont wear much from normal use, they are designed to slide pretty much forever, unless there is some kind of health problem, impacts or improper movement causing excessive wear.
So it could be normal stress, or it could be a problem. If you really have a concern, I recommend talking to a doctor and doing some research. It could be a number of things, including 'normal'.
