Some certifications are useful. Make sure you research any that you plan to go after — It doesn’t help to get a certification that companies look down on.
One of the best ways I have found to expand your network is to find a non-profit that needs a design project done. Do the project well, and you will get visibility. Ask from day one if they will give you visible credit for what you do. (Been burned by that nonprofits that take the work and “forget” to attribute it to me.)
You don’t need to personally have a big network. For introverts especially , find a set of connections who will talk up your talents and help you get your work out there where the right eyes can see it. Even better is the connection/friend who knows people looking for your skills.
If you are on LinkedIn, for example, ask people to write a recommendation for you. Ask them if there is someone in their network that you should know (and then ask them to connect you).
Hope this helps!