Welcome to the world of marketing.
I have worked in different marketing positions a lot in my life, and it can be a demanding occupation. You have to do your own research, start your own projects, and sometimes invent the product itself
I'm new to SEO as well, and only doing this as a sideline. That being said, I think a sitemap is a must. You can better check what pages are listed, etc by entering a "site: www.whatever.com
" search. There are many places that will make you a sitemap for free, and indexing is much more efficient with them.
A few links might not be enough. Really popular sites have 5, 6, 7 figures linking in (that's up to millions)
If you are operating with some resources, why not create your own directories, industry resources, etc. Won't cost you much, and can be done easily if you have an industry database already.
Also, is the HTML itself properly SEO'd? Good short titles, well done meta tags, etc. Not that I think it matters all that much now days
Hope this helps. Remember, content and usability is king, if people like or use the site, links will appear on their own.