You appear to have achieved recording nirvana. Everybody posts about trying to remove room echo from a recording (which you can’t do). Adding it is a snap. You can get some depth by making the recording stereo, splitting it and delaying Right with respect to Left. You can also gently add “Effect > Echo” or “Effect > Gverb” to the sound.
That was the good news. We can’t fix a broken singer. If they have an adenoid infection or sinus condition, you’re kind of stuck with that.
Post some of the performance here. Sometimes your description of the problem is far worse than reality.
I’ll post one, but I encourage you NOT to listen to it!!
The project is simply that I wanted to record some lullabies for my kid, for when she will be away on a trip. So I put the iphone on my chest while I sang to her one night. I AM NOT A SINGER, and the the singing is intentionally languid and boring, for the purpose of getting the kid to sleep!
I just thought it would be nice if I could make it a little less painful…
If you’re really keen make a pop-shield … Pop filter - Wikipedia
[ Approximate arrangement : mouth (six-inch-gap) pop-shield (six-inch-gap) microphone ]
If you can’t re-record IMO other software does a better job of reducing hiss noise than Audacity …