Hey there! I'm not an expert on promoting comics or anything, but as a self-published writer or a children's book and e-book, I think keeping updates and "hype" is important.
With my writing, I try to share either updates on story progression before it comes out to the public, ask for ideas/keep fan base involved, etc. From what I read, you are already sharing your work which is good, but maybe you could also add sketches showing progress, take polls, etc. There is no clear cut way to promote your work except finding the right place where you feel works best. This also goes for how you want to promote your comic, as you mentioned some people post entire strips. In the end, you just have to know how much you want to share, how you share it, and making sure people can see it.
I know this all seems basic, but for myself, I try to look at my promotions of my work through the eyes of the audience I'm trying to get it out to. If you can find a balance between everything I mentioned, it should fall into place. Of course, time and patience is vital because it may be slow at first. In terms of social media, I don't think there is a right place, just where your audience is. I would also look at forums of websites you might be on and try to promote there as well not just social media. It could lead to people going to your social media after. Hope this advice helped!