The changeover from chemistry to chemical engineering isn't as straightforward as a lot of people think. I don't know what your coursework was like to get your chemistry degree, but there are some differences: fluid dynamics, mass transfer, reactor design, process control & design, LOTS of thermodynamics, etc. From what I know, you'd likely have to take some undergrad courses first because a chemical engineering master's typically just expands on the undergrad classes. That said, there's plenty of people who just get a second bachelor's in chemical engineering, which is nice because you wouldn't have to take things like physics, multiple chemistries, and some of the math classes.
A lot of chemical engineers with bachelor's degrees work in either production/manufacturing environments or at processing equipment designers (heat exchangers, pumps, etc.) That's usually where you start until you build experience, so if this isn't something you're looking for, I'd go consider another direction. Personally, I love working the manufacturing floor. I get a good mix of desk and hands-on work, and in a lot of cases you'll get technicians under you to help. But if you're not interested in at least starting there, I'd probably suggest a different route.