As a Chemical Engineer, there has been little impetus and thus benefit to obtaining a PE license unless you work for the government or a consulting firm. Unlike some other enginering professions (civil, mechanical, electrical) chemical engineers are gennerally able to practice very well without having a PE license. Since you are a computer enginering major, that may be a bit different. However, I suspect your position will be much like mine - I worked for several firms over my 30 year career before getting my PE after I decided to set up my own consulting company.
The MS definitely helped me at various points in my early career. It brings a feeling of advanced learning and increased preparedness for your chosen career. While this varies by state, I believe that some require several years experience working under another PE before you can apply for your own.
If you think you may want your PE at some point, definitely take the FE exam now. I took mine when I was working towards my PE and trying to learn the other disciplines for the FE was a huge challenge for me!