I'm confused as to if I can sing or not?

Lately I have been really worried about how I sound to others when I sing. I thought I had a good voice for a while, until I started to record myself. I know that your voice sounds different to others as compared to what you hear when you sing. I get compliments on my voice sometimes and when I ask someone if my voice sounds very similar to the recording they say no. I have even asked my father if I had potential and he said that I did. I ask my parents if I'm bad all the time and they say no. I know that parents say that just to shut their kids up or to make them feel good about themselves, but my parents are the kind of people who would tell me if I sounded bad. My mother even told me so. However, when I record myself I sound like a five year old who's trying to sing good. When a recording is played back it sounds as though every small sound I make is exaggerated, and that my pronunciation of "t","ch", and "s" sounds are also exaggerated and pretty annoying. I've tried the thing with the two folders (that you put in front of your ears) but I'm convinced it is faulty because I sound even better with the folders and terrible on tape. Can someone please explain? Also, I'm using an iPhone 5 to record if it matters.

Posting a recording along with your question would greatly help! Also, family and friends aren't always the most honest, especially when it comes to an area as delicate as this. If you find something that you don't like about your pronunciations, change it. Record those certain areas over and over again, altering the vowel shape each time until you get a sound you like.
But recordings never sound as nice as the original, so it might not really be a big deal!

Provide a recording, and everyone has some special voice, they just need to practice on it.