If you have access to a college or relatively large public library, you can find in the Reference section a series of volumes that contain excellent literary essays that analyze myriad works; these are called Contemporary Literary Criticisms . Also, although you can access other criticisms through JSTOR and ERIC; most of the articles/essays that you locate are ones that have been published in reputable literary journals, and were not just published on the internet (this may be the kind to which your instructor is objecting). Thus, any articles published in literary magazines or books such as these are "non-internet sources." When you look up criticisms, just verify the source, as the journal articles will be mentioned. These you can locate also in a college library or on a virtual library site.
As far as your choice of topic, why not find some worthy articles and read them first as doing so often "jump starts" your imagination and often provides a starting board for you. For example, you may come across an analysis of Gothic elements in The House of the Seven Gables. But, you could also analyze The Scarlet Letter as a Gothic novel since the forest primeval is rather mysterious, and the Gothic element of victim/victimized exists with Roger Chillingworth and the Reverend Dimmesdale. Certainly, too, there are elements of the supernatural, and Pearl is not exactly a normal child. And, if this topic appeals to you, find some articles/essays on what constitutes Gothic and an enumeration of the elements of this genre.
You are writing a research paper which utilizes literary criticism and you have to use several "non-internet" sources. The term is a little tricky because I cannot tell whether your teacher wants you to stay completely away from anything on the internet or if you may use the internet to find some scholarly writing. For example, if you found an article about Nathaniel Hawthorne's writing style in a journal called Writer's Digest, would you have to find the actual print article or would the same article online (via the internet) be acceptable? I have no way of knowing that, so be sure to ask for clarification.
Generally, an "internet article" refers to something written by an unknown source or a source lacking literary credibility. These items might come in the form of a blog article, another student's essay, or even a teacher's class notes on the subject. While they may contain interesting or even valuable insights on the subject, they are not what might be considered "scholarly" writing. I suspect this is the kind of material your teacher would prefer you did not use. Again, though, there are plenty of scholarly sources which can also be found using the internet, so get some clarification from your teacher before you assume anything I have said is correct. To help you kind of sort this out, I've attached two links to sites I think might help you determine what is and is not acceptable in scholarly research. As always, however, your teacher must have the final word on this because it is his or her assignment.
Once you determine exactly what your teacher means by the term "non-internet," I would suggest you visit your local library and ask the research librarian to help you find the resources which your library has available. Research librarians love to help and are the most knowledgeable resource you will find to help you. They will show you how to find scholarly articles and search various databases for the things you need. Being able to sort information and find what you need, in this case scholarly articles, is a wonderful life skill, so look at it as an opportunity to increase your "life tool box" with another useful tool.
In terms of these two Nathaniel Hawthorne works, The Scarlet Letter and The House of Seven Gables, you have many choices from which to work, it seems to me. The most logical research format for two things is to compare and contrast.
One strategy might be to find three or four (whatever suits the length of the paper) points of comparison and/or contrast between the two novels. For example, you might compare and contrast writing styles, themes, characters, or whatever else you might think of after your reading. An outline for this kind of essay would look something like this:
I. Writing style
A. Sentence structure
1. In Scarlet
2. In House
B. Figurative language
1. In Scarlet
2. In House
and so on. Another strategy might be to deal with all the points of comparison and then all the points of contrast. In this case, the works are probably more alike than different, so the kind of outline I started for you might work the best.
Another idea is to think about both novels in terms of Hawthorne himself, examining when he wrote each novel and whether that had any influence on either novel or perhaps how his personal life was entwined with either of these works. This might be a little more difficult to do, but it is interesting to study.