Hi,
Yes, you are eligible to study aeronautical engineering. You are eligible for lateral entry in the second year of B.E/B.Tech.But, there are limited colleges offering aeronautical engineering.
You can continue in your disciple too. As the future scope for the mechanical branch is more when compared to the aeronautical up to my knowledge. It is up to your interest if you are more passionate towards it.
You can know more about aeronautical engineering, offering colleges through the link: http://engineering.careers360.com/articles/aeronautical-engineering-2