I'm not sure I agree with you. Being able to acknowledge temporary weaknesses and overcome them can be what defines the happier moments, IMO. This is just based on how I am and from my experience. As long as you don't wallow and swim in self-pity too long (1-3 days tops), I don't see any harm in it.
Try your hardest to get yourself to the gym so that you can get some endorphins released by working your butt off, even if it's for 20 minutes. It's like an instant happiness makeover if there ever was one. And if you've been moping around already, have you been following an irregular sleeping schedule? When I was dealing with depression, I took a long hard look at everything that triggered all the negative emotions in me (took me about a year and I'm still learning new things). Poor sleeping and eating habits are my biggest culprits other than issues that are beyond my control (family and etc). For me, those are things I forget to focus on when I have so many other stressful pre-DO things to worry about. Perhaps look into yours, it might be exacerbating your situation.
Read stories about successful entrepreneurs and businessmen who made it from nothing. A lot of people have difficult situations but they don't let those situations define them. They use it as a way to find hope of something better. Read/watch stuff about athletes who sacrifice a boatload for their goals. When I compare myself to people like that I feel ashamed for feeling self-pity. Maybe you might feel the same. I'm sure you know Ruth Bader Ginsburg still fulfilled her duties while doing her chemotherapy.
OP, give yourself one day to yourself to do whatever you want. Fall into a book and forget the world, get lost in a video game, or just hang out with people whose company you enjoy. For extroverts especially, hanging out with people whose company you enjoy and whose ethics you value, might be just what you need to get yourself on two feet. Something that I want to add is not to over indulge in an excess of bad food. I'm not sure about other people but overeating crap makes me feel like crap the next day.
Also, this is what you want. After your day off, I do agree with nontrad78 that you should grab those interviews by the throat and own it. They're clearly interested in you, now you must return the favor. There are plenty of books, thread, and advice about acing interviews. Get on it
TL;DR - give yourself a day off to do anything and everything that will temporarily make you forget about your situation. Try not to overindulge in crap food and try to sleep properly if you aren't. People underestimate this, but it really affects a lot of people. Immediately afterwards get yourself motivated by remembering why you are doing this and not to forget about what you want. You made it this far, you owe it to yourself to continue and let the self-doubt fall to the wayside.
P.S. my name is ruth! Hahah.