You are right to be concerned, because sometimes new moles can be a sign of a developing melanoma, which is a serious form of skin cancer that needs to be detected and treated early.
That being said, it is normal to continue developing new moles in most people even into their 30's. After that, new moles are less likely to be normal. So, in part, the answer depends on how old you are. Also, it is common to "miss" a mole in a location that you do not normally inspect regularly (such as the underside of your arm); it is entirely possible that the mole has been there for a while and that you have just not noticed it until now.
Nevertheless, the following characteristics of any mole should prompt immediate evaluation by a primary care doctor
or by a dermatologist
(called the ABCDEs of moles)
1. Asymmetry (if the mole looks lopsided)
2. Border irregularities (if the mole has a jagged or otherwise unusual outline)
3. Color changes (for example, multiple colors inside the mole, or a new dark spot inside an old mole)
4. Diameter (any mole larger than the size of a pencil eraser is concerning)
5. Evolution (any change in the way a mole looks)
Again, please see your doctor or dermatologist about this issue. Good luck.