What works for me:
1. Breathe. Panic attacks for me require deep breaths, drinking a bottle of water, drinking a cup of tea/coffee, or other familiar comforting experiences. Buzzword to Google here is «parasympsthetic nervous system».
2. Reflect. Reflection confronts is with truth. The fact that you are asking us proves that you know that the truth is, these fears do not define you, they are not anchored in sober reality. I sometimes do long-form reflections like journaling but usually this is a short-form reflection. I come from the Christian tradition so the easiest one for me is «I am a child of God.» I will repeat that to myself, gradually creating space between the repetitions to reflect on it. “I am a child of God, my worth is not defined by [my parents/this class/my next performance review/my wife/whatever]. I am a child of God…” But some will instead do «five whys» reflection or «om Tare tuttare ture svaha» or I used to, as an atheist, recite my Five Commitments to give myself space to reflect on reality and my distance from the current situation.
3. Get information. «Information can only help, not hurt.» So I might dread looking at my bank account balance for example. It's important that I remind myself that this is kind of silly. The balance is not going to be magically higher just because I'm not looking at it. The balance is whatever it is right now, my monkey brain needs explicit reminders, “If it's bad, then knowing how bad it is won't make it worse.” I might find out that there is less to do than I fear, or my fears might be confirmed but I will know more so as to plan accordingly.
4. Mental offloading. What do I do with that information, do I sit on it? Allow it to marinate my head? If it is actionable, like what to do on a project, «I better write it down!» Every moment some new obstacle arises, write it down somewhere. Google's “Keep Notes” works for me. Writing allows us to extend our brain, give it an extra heap of virtual memory. A phone alarm gives us a coprocessor: I will set alarms to remind myself to get the baby to sleep, to re-park the car for street sweeping days, to take out the trash on trash days, even to take medicines, religious upkeep, or practice guitar. Another powerful tool is the checklist, you might want an alarm that tells you to go through a checklist of housecare activities, or you might have a morning checklist, or you might have a shopping list. “Get it out of my head!”. It is clutter! Offload any mental task you can.
5. Get your foot in the door. When we were growing up we would shut our brothers out of the room, close and lock the door, but if they saw us doing it, they could put their foot or a shoe or something else in there, we could not get it out without relaxing the pressure. «I just need a little opening.»
Find the smallest task you can possibly start on in this project. You do not need to parcel the whole project into small tasks, (but if your brain works that way then more power to you). But my way is just to peel off a tiny chunk and work on that. The great part is that I know I'm tricking my brain and somehow my brain still lets me trick it. I know that once I'm doing that small thing, I will discover that this can't happen until something else happens, and I will go work on that other thing, and give me 15 minutes and I will suddenly be in a flow state handling the entire project, I can't help myself. But when I'm outside the project it seems like too much. But when I'm inside, time flies. «Getting Things Done» calls this a “next action”.
To those five pieces of advice, I will add two more that have to do with different situations than you have asked about, but they often coöccur for me with the situations that you are describing.
6. Clear the buffers first. The previous step is not terribly helpful in figuring out how to start on a hairball. If you have ever dealt with an extremely messy room… Oh have I lived in some messy places! Here is my first lesson: «Always start by identifying & clearing the stashes.» What is a stash/buffer/queue? It is any place where you put things with the intent of bulk processing them later. Laundry hamper (to wash later), dryer (to fold later), sink (dishes to wash later), dishwasher (to put away), trash bins (to take out later). Because sometimes tasks really are bigger than the time you have right now to devote to them, and you need to take the step which has the most leverage. Well, if you don't empty out this trash can then you have a buffer overflow situation for trash, it starts to appear on countertops or floors or desks because you don't have space in the trash and you don't have time to figure it out. You don't have space to put dirty dishes because the counter is full of dirty dishes. [You can also stash tasks!! But you have to make your stash clearable which requires a different sense of what a task is. “Schedule time for X” rather than X itself. Remember, it's only a sash if you use it for bulk-processing.]
7. Then, try to minimalize. Marie Kondo’s bestseller attacks mess from an almost anti-Christian perspective, “what would it look like if you really loved your stuff with all your heart”? Powerful materialism. The surprising thing is that it comes to the same place that a Christian would, because they are both careful to center Love. If you really love each thing that you own, then you will know it by name, it will have a beloved place in your drawers where it lives and belongs and can thrive, and whenever you pick it up it will be something that you can take joy in, much as you would take joy in interactions with your children or spouse. Well, not everything is like that, sometimes you don't take pleasure or joy in having a plunger, but you need a plunger just in case your toilet gets stopped up. «Give up all you neither need nor want.» Be honest with yourself about, will I use this in the next 6 months? 1 year? Do I need this for emergencies? My parents miseducated me: that's a “perfectly good ” such-and-so, I can't throw that out! Do I want it, in the sense of does it give me pleasure and joy just by being in my life, whenever my eyes dance upon it—and if it's not, then, does it fill a legitimate need for which prudence demands I keep it anyway. This is also true our emotional damage, but that would take a lot more to get into.