I like working with my hands as well. When I was younger I loved building model cars, and then working on real cars, building model airplanes, building structures. When I was considering what I wanted to study in college I wanted to make sure that first and foremost that I was going to enjoy what I was going to learn and that it complemented my desire to continue working with my hands. I found that engineering was for me because I was able to work in a lab and build experiments with different types of equipment. There are many fields in engineering that will allow you to do this.
Juan Ramon recommends the following next steps:
Have you considered Computer Science? I've always described programming and development as "problem solving with a well defined set of rules". You're constantly being challenged to not only solve problems, but to help people really understand the root cause of the issue they are attempting to solve. It's a fun and challenging career.