Your chances of getting into a good ChemE graduate program are dependent on a lot more than just GPA. Specifically, your GRE scores, recommendations, experience, application/SoP and the X-factor. If your 3.8+ GPA is reflected in your GREs, they will probably ignore the bad semester you had. Recommendations are important because it shows if you are a standout student to your advisors/professors/whoever. Remember that your competition will receive similar recommendation letters, yours needs to be different. Experience could help since you've already co-authored two papers, any work experience would be helpful. Your application/SoP should focus on you, what makes you want to attend graduate school, why you want to attend, what motivates you, what your goals are, etc. Lastly, the X-factor is something you can't control, i.e. the number of qualified applicants to a particular school in a particular year, availability of funding, availability of professors, etc.
MS and PhD usually only differ when it comes to funding. Keep in mind that some schools don't accept MS/PhD students, you'll have to get a MS, THEN apply for the PhD program.
As for your school choices, I'd consider MIT, UDelaware, Cornell, Columbia, Georgia Tech (it's not NE, but it has GREAT funding and opportunities), etc. If you branch out and look at the midwest you can consider UIllinoisUC, Purdue and UT-Austin.
Hope everything works out!