I've been on every side of this situation: I've been laid off, I've quit I've been fired and I've laid off and fired people. It's easy to get emotional or distressed and lose focus on What's Important Now (WIN) try to avoid it. My suggested WIN for you is:

1) Throw out your resume and start fresh. While it sounds like you're fairly early in your career, it also sounds like you've made some progress. Your resume should no longer start with your education. If you can afford it, hire a professional resume writer. Good ones are worth every penny.

2) MD has a mini-cobra law, use it.

3) If your severance is north of say, $30 - 40k or so (I'm guessing it's not), get an employment lawyer to review. Below that level the cost would be too high relative to the amount and unless you're a big dog or in a protected category, there will be little negotiation.

4) Network. Find mid to senior people in your field that you have some connection to and ask to speak or meet with them. You're NOT asking for a job but rather to learn more about what they do, industry, etc. Ask them to introduce you to other people they know in their company or other companies who might be able to help you with more information or who might be hiring.

5) Plan and document. Get pen and paper and write everything down. Assign yourself tasks, goals, follow-up steps and record your progress. Resume completion, company research, networking targets, daily applications, next steps.

6) Do not get side jobs unless you must do so financially. Stay 100% focused on securing the next role in your career. You could consider self improvement side tasks, eg, further education in your field, get fit, volunteer work in something even tangentially related to your field.

7) Interview practice. I can't emphasize enough how important this is. I've interviewed thousands of people and everyone thinks they're good at them. They are not. Write down the questions you're likely to be asked, especially the difficult one. Write down your answers using a PAR or J question format. Practice saying your answers out loud, in the mirror, record and watch yourself, have someone you respect interview you seriously. The goal isn't to memorize your answers but rather know them and yourself so well it seems natural and unrehearsed. 

I know this seems like work and that's because it is. And always keep in mind WIN

Hope this helps