There are so many different types of arthritis, more than 100. Unfortunately we are not doctors here and cannot tell you what type of arthritis you have.
In general, when people use the generic term "arthritis" they are really talking about osteoarthritis. However, there is even a subset of osteoarthritis which has an inflammatory feature making it resemble RA. It can get very confusing indeed.
You really should consult with a good rheumatologist. This would be the type of doctor who could help find an accurate diagnosis and get you started on an appropriate treatment.
I know that you are probably worried that you will end up with hands that look like your mother's. With proper treatment, they may not happen and treatment options for RA have changed dramatically in the past decade or so. Don't give up hope, but do keep looking for answers.
Lisa and Ronie are right - you need to see a rheumatologist to find out what is going on with your joints. if you have rheumatoid arthritis, it's important to get treated so you can prevent the kind of deformities that make your joints crooked or have limited range of motion. Please note that if you're talking about RA, your mother's experience doesn't have to be yours - there are a lot of treatments for RA these days, so there is every possibility that you will be able to avoid deformities. If your mother have RA, it is also possible that her disease may be suppressed, which can prevent further deformities. On the other hand, if she has osteoarthritis, you may want to show her our osteoarthritis site where she can find more information about the condition.
I agree is Lisa, a good rheumie should let you exactly which type of arthritis you have been dx'd with instead of being so vague.
What exactly do yo mean by "crooked?" I have been dx'd with 2 different types of arthritis. A couple of my fingers are "crooked" and some are "twisting." The ones I call crooked have the tip joints that are permanently bent downward. Xrays and mri's have given docs enough info to tell me this bending is caused by osteoarthritis. The fingers I have that are twisting do not point forward when I hold my hands out. They kinda point sideways and I have had to change my grip. This is my RA. However, my mom's hands did not look like this.
So what I am saying is the type of swelling and joint movement can help determine the type of arthritis and where.