If you are going to be an English major, take all the technical writing courses you can find and work extra hard at getting the computer experience. There are even schools out there that offer a technical writing degree. Most companies look for at least a 4 year degree. When I was just entering the field, my 2 year degree got me in the door, only because I had the computer experience. And, as I progressed through the years, that experience counted more and more.
Experience is what counts the most.
Try to find a company that is willing to let you intern while you learn on the job. You need to have a very thick skin to be a technical writer. Every person who edits your work thinks they know how to write and are determined to be critical. Get used to it. Don't take it personally.