The design industry is no different, 99% of the work you do as a designer is boring and repetitive. The same is true for agencies, they might have work for big brands in their portfolios, but that work could be years old. It's more likely their day to day workload involves dull, corporate work (often pharmaceutical companies) that keep the lights in the offices on.
I started by applying for a design degree course and seeing out freelance projects whilst in my second year. By the time I graduated I was able to work full-time for myself due to the client list I'd built up, whilst most of my friends sought out work in studios and agencies. Personally I prefer self-employment, but the stress that comes with running a business by myself is probably affecting my health too.
I'd start my reading articles and books on the subject of graphic design and start designing stuff for yourself and perhaps look into a course if you feel you need extra training. Design isn't really an industry you can just jump into without experience and the same is especially true for architecture, but you get experience by learning and doing so get out there and do it!