Looking for work is hard and exhausting. I don't know how many jobs I have applied for or resumes and cover letters I have sent out. It's probably in the many hundreds. I have also been on countless interviews that have led to nothing. Don't take it personally. My advice is to work on your resume and come up with some interview answers to be prepared when you get to that point. As far as leaving your last job, can you spin it as lack of opportunities or growth without being untruthful? I'm not suggesting lying at all. You have to make things into a positive. Lack of challenges, more aligned with your degree, etc. I have said things like the position didn't materialize into what I had expected or after starting I realized it wasn't a good fit and after speaking with my supervisor thought it was only fair to myself and the company to resign.
Working on your networking is important too. I'm so shy but I try to use my strengths like being friendly, listening well, etc. I always trying to incorporate any good advice into what I am doing. It is very difficult. I also find working every day difficult. I cry, I get so physically sick with worry, I get shakey, dizzy and sweaty. I don't like it but I don't have a choice. Don't give up on yourself.