Could you please explain the differences between Civil, Architectural, and Mechanical Engineering? Also, could you suggest which one I should possibly take?

The real question is what are your non-math interests. There are a ton of lucrative and interesting careers based on mathematics. Unless you are specifically interested in mechanical devices, buildings, or civil structures (buildings, bridges, highways, etc) I would consider looking more broadly.

Mechanical engineering will use the most high level math skills of the three careers listed. Architecture and Civil engineering also have a large component of knowledge and application of local and federal building and construction regulations and codes. Civil engineering also has environmental components such as rain water drainage, soil characteristics, and environmental regulations.

What type of math (calculus, algebra, statistics, etc) do you enjoy the most? What other areas interest you? Computers, mechanisms, electronics, robots, building, homes, etc? Those questions will help you narrow engineering fields. Also consider things like economics, statistics, finance, and data analysis. All of those fields are respected and heavily involve math but do not necessarily involve engineering.

Based on the careers you've mentioned above, the highest paying one, on average, would be Mechanical Engineering. You're going to have to be good with math no matter what. Civil Engineering is the design/construction of the physical environment. Mechanical Engineering is the study of operating machinery. For these two you will take a load of physics, and material science classes. They are great fields since you're good with math.

A lot of interesting comments. It is not just about your academic interests, it is about your passions. If you are fascinated by buildings and bridges, then architecture or Civil Engineering, if you are interested in all areas of physics, Mechanical engineering is a study of applied physics. I do product development because I like creating new products. I am in medical because I like making products that have a positive impact on peoples lives. But Mechanical engineers have a lot of choices in career paths.

Find you passion, follow the education path that allows you to work in that field, and you will enjoy your work life.

Here is a site that will tell you much about engineering and the different types of engineers that there are - except the ones that drive trains.

http://www.huffingtonpost.com/marjorie-hansen-shaevitz/so-you-want-to-be-an-engi_b_5508385.html

Let me know what you think about it. I would like to help further, if I can. Send thank you notes to those who help you.