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:
- Improve your math and logic skills. Again there are a lot of online resources to help you with both of these.
- Lean computer science fundamentals. These include data structures, etc. Buy the book: 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.