No, you're never too old when you're starting something that will be a hobby and something fun. You're most likely to be placed in a teen or open class made especially for people who are just starting ballet, people who are not as strong as others in their age group, or people don't wish to commit to a serious class that meets more than once a week. Your body type won't really matter then, but it's good that you're in shape.
Ballet being boring is based on your opinion of 'boring.' Yes, many ballet exercises are slow, but that's because ballet takes loads of control. Also, your teacher may teach some of the movements and combos very slowly. This is only to get the dancers to fully understand the movement and to get them to use the right technique. Ballet can also be very fast and lively. Many exercises are very laborious, and will leave you out of breath sometimes.
Don't worry about fitting in. The other dancers are in the same position as you. They are all there to just have fun and learn something new. The class will give you something to talk with them about, and there's bound to be someone who is shy also, so just strike up a conversation with someone. If nobody wants to talk, then just as well. Focus on your dancing.
For your mother, I think you should let her know you're serious about this. She wouldn't say those things if she knew that you were really interested about ballet. Do some research. Find a dance studio near you that has a teen class, check the prices, and tell your mom. Maybe look up some videos of ballet dancers online for her so she can see that ballet is not boring, and not for little kids.
I hope this helps. It's good that you're trying something new. Good luck!!
Dancer since I was 3