I don't like to promote myself either. I'm the type that tends to stick to the background and work behind the scenes. There is promotion/marketing you can do without directly being in the forefront.
If you haven't already, look into Search Engine Optimization for your website. That looks at how your site is showing in Google search result rankings and tries to bring it to a more favourable position. There used to be some good free SEO analyzers out there, but I'm having a hard time finding ones that show extensive stats.
You can also look at Google Analytics which would give you a whole bunch of stats on the website. It can give insight on places that might need to be optimized.
In my experience, the ones who last and are successful are those who stick it out. Overnight success is extremely rare and based more on luck than anything. It's dedication and perseverance that make the biggest impact.
We see it here on Medium that the people who end up being the most recognized writers are the ones who have been around for a while. It's the same with a website or a business. Slow but steady growth is sustainable and helps to ensure you're not overwhelmed. Eventually, it leads to dedicated fans and buyers that will share your stuff themselves.
With that said, define what success is for you. This helps to create goals and provide focus even on days where things seem hard.
I know it sounds cliché, but celebrating small goals towards your defined success goes a long way to keeping self encouragement going, even on days where you feel discourage. Celebrate when there been 50 people to your site for example.