If your school has an alumni network, make use of it. Go to their events and listen to them talk about what they do, or at the very least, register on any alumni websites your uni offers. I didn't even apply to my current internship - they called me, because they saw my resume on the school career website (I posted it there, and they can use keywords to find students). I find that alumni are very eager to hire grads from their alma mater.
When applying online, you have to basically seed them out, as much as I hate to say. Before I was "invited" to my current internship, I had been to many career fairs and applied for many positions and got rejected for all of them either outright or after 1-2 interviews, and I have a 3.9 GPA overall. One of the guys who I had an interview with seemed like he actually wanted me to come there but there was only one position available and he said "90" people applied for the one position and I was his second pick. It doesn't matter that I was second out of 90 - only number 1 gets the job (its also possible he just said this to be nice but we had a second interview and talked together for at least 45 minutes over the two). Applying for more things increases the odds that you will get "lucky" - that is, you will be the one they select out of many similar candidates. Just keep at it and don't give up.
The problem with online applications is just this - there are so many people who can apply. You have to counteract this by sending out many resumes and cover letters. I know its a pain in the ass, and I know it feels like a total waste of time, but it is what you have to do. Stay persistent - believe it or not, good chemical engineers are few and far between and I'm sure there is someone out there who needs your help. Also look for less advertised positions - companies which always attend these events want to get 200 people to apply so they can choose the very best. Don't go straight to the companies who go to every career fair at every school, and don't only apply to companies on the big sites like Indeed, etc. Other companies who don't advertise as much may also be looking to expand and won't have anywhere near as much competition.
The thing about networking is that it isn't like sending out a job application - the purpose of networking is not entirely finding employment and employees - its to expand your vocational circle and get to know other people. I hate networking - I would much rather be at home playing on my computer, but it is good to know other people in your field, because you never know when they are looking for someone. You should try to really get something out of the discussion though and not just sound like you are looking for work. When people say they get a job through networking, its not after talking with them for 15 mins - its usually because somebody has known somebody for a while who can do them a favor. Think like the dad who gets his son a job at his friend's company.