The job search struggle is difficult. I can relate as I am job searching myself because despite having a full-time position, I am not happy. I think that the biggest thing I can recommend is to take a hard look at your resume. Cover letters are only read about 50% of the time, but they will always look at your resume! Depending on what field you are in, you should really consider making your resume stand out. Personally, I work in content creation and public relations and I have designed my resume to reflect my creative ability. Second, you should adjust your resume for each job. You don't need to make up things, but as much as possible, the bullet points on your resume should line up with the tasks of the job. Lastly, put specific results in your resume, a hiring manager should be able to know a few of the exact things that you achieved in a previous role.
Don't give up and don't settle! The right job will come around and sometimes there are first a lot of rejections.