Technically, no you do not need a college degree to become a software engineer. The most difficult parts of becoming a developer is in two parts; one, getting the skills and two, getting the job.
You have to decide whether or not you want to do it professionally. Each of these is strenuous and a long task. Many people after getting skilled take a year or longer to land a software development job. The skills itself is not the lone task.
Getting a college degree speeds up both the skills process and the job hunting process but that is not the main reason to get a degree. The degree helps most with confidence.