Should I get a Masters Degree in Civil Engineering?

I don't know that you would necessarily be able to get a higher salary at any particular job because of having a Master's degree. However, the biggest benefit that I found after getting my MS in Civil Engineering was that, in a tight job market, I had a significant advantage over the numerous BS applicants for the same jobs. Potential employers instantly bumped me ahead of similarly qualified BS candidates because in many cases it was the only distinguishing factor and it told them that I was serious aobut the field. It didn't really give me better negotiating leverage for higher salary but got me interviews for the jobs that I wanted and the higher paying positions.

As for ME vs MS, I personally would go with MS just because it is more widely accepted as a traditional Master's program.

You will be able to demand a higher salary with a Masters degree in any field. I think that you should go for it!