I totally understand your situation when you say that you feel as if something is blocking your throat. Many beginners face this as they try to sing certain parts of a song they can't fully grasp onto yet, and also encounter this if their singing ability has not been built up to the best potential it can be.
Like BLUEBIRD has said, warm your voice up and make sure to stay away from products that can make a lot of mucous build up in your throat. I also find it necessary to sing difficult songs to help make your throat and vocals more flexible to singing better. Singing is for sure something that takes a lot of time and effort to be able to improve on.
To go back to your point about the blockage in your throat, this might be due to the fact that you might be singing at a pitch higher than your natural voice. A tip could be that you could try to slowly ease yourself up to those higher pitches without causing a lot of "strain"* on your throat. And by easing, I mean to start off at a pitch you can actually sing in, and then slowly build yourself up by pitching the song however many keys/octaves you want it to to be. This will also help you be able to extend your vocal range as well!
And! The blockage could be caused by nervous tension. This could lead to that blocking feeling you may have in your throat.
Also, you seem very concerned about your singing voice and how it might appeal to others. Don't be afraid to sing around your parents, and by not being afraid, it could also lead you to sing more proudly. It's taken me 5 years to build up the courage to fully sing in front of my family, so I hope you won't hold back your singing voice to your parents. It may take time to build up the courage, but start off small!
*strain - where one's throat tenses up due to the inability to hit a certain note and causes the singer to have to use a lot of effort to be able to sing that note.