If you are truly interested in becoming a software engineer, I would not let your fear that you are not good in math stop you. 

Most people who think they are not so great in math just have not had a good experience in learning it.  In some cases it is made worse by societies that do not encourage females to excel in the math and science areas.

As Craig mentions below, most software programming tends to focus on Logic anyway.  You might not have a career in advanced algorithms, but there are plenty of jobs available that will not require that knowledge. 

I would start by doing a few main things:

1. Start learning computer programming.  You will need to be able to program in at least one programming language.  I would recommend learning Ruby or Python and also become familiar with Javascript.  There are a lot of online courses you can take.  I would also recommend taking one of the developer Bootcamp classes like Hack reactor or General Assembly if you can as they will not only teach you but help you get a job.
2. Improve your math and logic skills.  Again there are a lot of online resources to help you with both of these.
3. Lean computer science fundamentals.  These include data structures, etc.  Buy the book: Cracking the Coding Interview, 6th Edition: 189 Programming Questions and Solutions: Gayle Laakmann McDowell: 9780984782857: Amazon.com: Books study it and try to do as many of the examples as you can.

I think your should follow your dream; however, this will take some time (>= 1 year) so start now.

Good Luck!

See Questions On Quora