Yeah, it should be 2-aminopyridine, unless there is a functional group at the 1- position already.
Anyway, assuming that it is 2-aminopyridine, I think it is possible that either one of them could be protonated.
Protonation of the amino group would seem favourable because it is an sp
3 Nitrogen, as compared to the N in the ring, which is sp
2 hybridized.
However , as can be seen in the above pic, the aromaticity of the pyridine ring is retained when the amino group is protonated, but the positive charge on the N remains localized to it. On the other hand, delocalization of the positive charge is possible when the N in the ring is protonated, but at the cost of aromaticity (or that's what I figured)
So, it really is a tough call. But I don't know if I'm right. Can someone please check my answer?