Self branding and marketing is also incredibly important. It does not matter if you are looking for a job or seeking freelance projects, you need a brand that defines you. Make sure your website, resume, invoice, business card etc look professional and coherent. Create a logo if you want one - Use your cartoon style to create something that resembles you and your work for example.
Think about marketing yourself to companies. Illustrators are very rarely hired full-time, more often they are contractors. So find companies in your area, that you would like to work with and contact them.
But you are beaten by other illustrators constantly? Well, we are living in a visual world. If someone with inferior skills presents their work better than you, they will most likely get the job. How can you change that?
Work on your presentation. Stick out. Have a portfolio people remember. Send them something that is unusual, like a cover letter in cartoon format or whatever else you can think of. If you look online for cool self presentation ideas by designers and illustrators, you can find a lot. One of my favorites is the resume printed on a chocolate bar - If I would hire, I would be in love with it.
And lastly: Network.
Now this is a hard one for most of us, as many of us have more introverted tendencies and have a hard time to go out and meet new people. But if you want to be successful, people need to know you are here and open to take on projects.
Present yourself to your family and friends. Show them your portfolio, give them a businesscard or postcard. Often times you expect that the people close to you know exactly what you are doing for a living - More often you are completely wrong with that assumption. See if there are events in your area where you could do some networking. Look for recruiters in your field. Have an all-star linkedin page.
Interesting sidenote: According to a career manager I have worked with, only about 10% of open jobs are posted online. 10% are sitting with recruiters, 5% are found some other way that I forgot and a whopping 75% are found networking. Now you understand why it is important to go out into the wild.
Finding clients/work is often a job in itself. Having been in a similar position (I will start my new job next week) I can totally understand how hard it is to lose a job you love. Take the time you need until you feel positive about the challenges and opportunities that you will find in the future. Then work on a branding you are proud of.
I wish you the best of luck, although you won't need it if you work hard.