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Are you people oriented? Or are you more interested in the chemical process side of things?
ChemE is wide open. Sometimes, the best thing to do is to just find a gig in an area where you'd like to live. Then commit to working at it for a couple of years. If it's a people oriented gig but you like the actual process part, your company might have options to try out other areas that might be more suited.
If you like food, the food industry has a lot of options - Kraft Foods, Unilever, Mars, Nestle, ConAgra. The chemical industry has a lot of options too.
A ChemE degree is a great jumping off point for a future. And remember, trying something out for a first job isn't a committment to a life long career in it. Sometimes gathering experiences can lead to a more well rounded resume.
If you like people and find that managing people is interesting, then there are opportunities for that once you've put some time in "doing".
Keep breathing. If you wind up not liking what you're doing, at least you'll have a paycheck coming in as you search for a new gig.
I like to look at jobs as something you're trying. Most positions in a company morph from what you start out doing. If you like the company you're working for, many will work with you to keep you if the fit is good and if you put your time in.
For example, if you start out in the manufacturing plant working on troubleshooting a process, you might find that you're enjoying working with the other engineers and you find that some of HR stuff doesn't bug you and that you like helping people. You can advise your manager that you might want to try a management experience to see if you'd like that.
Doing your given job matters too. If you perform well at what you are doing, companies will often give you other opportunities to change and grow. If you're underperforming or have a poor attitude or "don't fit", then it will be a problem to ask for other growth opportunities.
Is there a type of product you like? ChemE touches so many industries.