Hey, thanks for sharing your story. Hearing all these personal experiences does put things into perspective for me and realising there are many people like you out there.
I don't think you should get too hung up about having big name companies on your resume. As a anecdotal data point, I worked in 5 companies till now and 3 of those companies are internationally well-known yet even I am in your shoes - no callback or interviews.
As others have said in the thread, before considering doing a masters just for the sake of it, spend some time:
- persisting with your job applying. Sometimes it is just a numbers game.
- start working on your own personal side projects.
- get involved in the local <$programming> meetups, communities, conferences, etc
Good luck!