Practical suggestions:
YES, try to negotiate incompletes with your profs; YES, talk to your advisor; script-wise, say something along the lines of having a moment of being overwhelmed during the semester (without going into details) and simply explain that the getting behind on assignments just snowballed on you. I'm not sure what the terms of your type of scholarship is, but I agree with Hops - they know you CAN perform, so the worst that can happen if you ask them for help w/support resources would be a "sorry, no, we don't do that".
You are not BAD, not necessarily depressed & anxious - beyond your control, because you're struggling with things at the moment. Everyone I know - including me - is struggling with things. It's all relative, dear. That's the problem with labels; they don't describe degrees of a thing - you either are or you aren't.
Everyone in an academic situation, including faculty & staff, have a degree of "fear of failure". Students worry over grades, completing work (you'd be surprised how many incompletes there are every semester even when things are "normal"). Faculty worry over student/dept performances reviews. Staff are also subject to reviews. Seems everyone in that environment is being measured, graded, held up to some ideal standard which is NEVER clearly defiined.
Some of that fear of failure's usefulness, is supposed to be motivation. LOLOLOL. But there are ways it's counterproductive. I know my way; you have yours. It's time to take your lemons, and make some lemonade. And then DRINK it... and enjoy it. It's not going to make you happy all the time (such a thing doesn't exist) but it WILL make you happy and relieved to have dealt with the current situation constructively - obstacle was bigger in your imagination than reality - and clear that obligation and move on with simple joys. Daily doses of this or that, that you enjoy. At least for a little while.
IME, happiness is a state that simply happens to a person. It lasts a moment, a day, a week... it MIGHT be related to something in concrete life; it might be you simply let something go and now the sun is shining and colors bright... but it doesn't HAVE to be. There is no science of happiness. No system that works for everyone. Playing with rocks - heavy as they are - makes me happy. But not everyone enjoys physical work.
My definition of "happy" is usually more like contentedness, relaxed, working in the "flow", or having accomplished something that mattered to me; that I WANT. And I've slowly trained myself to take care of the things I dislike or make me uncomfortable, as soon as possible, as efficiently as possible... so I can go do the things I like or need, to take care of myself.
You're learning, even when you don't think you are.

Fret not; this will all be OK and you'll get past it.