I was trained in singing in elementary school and then again in high school.
I made an honor choir or two. (This would be a significant accomplishment if I was female, which I am not. They'll take pretty much any boy who can hit the right notes.)
Years ago I recovered from a cold except that the phlegm in my throat didn't go away. It is still with me. If I try to sing, my voice will just cut out on certain pitches, and sometimes I'll get a gurgling effect from the phlegm.
I had a voice teacher who was also an opera singer, and "singing when you have a cold" was a very common problem for him. Every singer has to do it, so I'd encourage you to consult one. Good luck.
Most people can learn to be decent at it. A few really are tone-deaf, but not all that many.