Putting it off until such time as you’re not stressed, not busy, or not distracted probably ensures that you will put it off forever.
It’s probably always going to be inconvenient or difficult to make time for writing if you are trying to carve out room for it in an already packed life. And the fact is, you’re probably going to have to do that if you ever want to find/make the time because there is rarely an ideal time to write.
That said? Do exercise self care. Don’t force yourself to do it if it’s actually making you unsafe, unhealthy, or beyond uncomfortable. Writing is supposed to be hard at times, but use your judgment. The point is to not use “I have too much going on” as an excuse. If it’s an excuse, you can get past it. If it’s the reality, take care of yourself first.