Is it normal, to have a inability with music?

When I was much younger, my family told me that I had to take music lessons. I wanted to take guitar, but my grandmother forced me to picked piano. I took piano lessons for 8-10 years and in those years I couldn't play. I couldn't read the music and nor could I remember it. It would often take weeks sometimes months just to learn one song and move on. It was very hard. I couldn't remember what key symbolized what letter. I found it impossible to only look at the book or have a conversation while playing. If I did, then it would result in me messing up.

I tried to write the letters on the book and I would often get them wrong. My grandmother and sometimes my teacher would get upset with me for writing down the letters, saying that by then I should know them and that there was no excuse for it. When, I moved onto a book that contained broadway songs, I did allot better. But I still couldn't read the music. I remember, I tried to play Beauty and the Beast, but I couldn't read or play anything and I got so upset that I banged the keys and cried. It was the same way with the "Music of the Night" and "The Phantom of the Opera". Those were my favourite songs to play and I was obsessed with them. It took awhile for us to master the pieces, but then I found that I couldn't play those songs at home. I could only play and read them with my teacher. When tried other songs in those books, but it was impossible for me to play them. It got to the point where I was scared to move on and I sometimes ruined my chance to move on to another piece in the book.

Every time, I had a class or left his class, my knowledge, everything I had previously learned would be completely forgotten. I was taught many misconceptions, but I'm not sure they were the cause of this problem. During the years, I had grown to hate piano and I was literally forced to continue it. I later found out that my grandmother wanted me to be a famous pianist, which greatly upsets me... A few months after I had completely stopped taking my lessons, I attempted to play "The Phantom of The Opera" and to my horror, I couldn't remember it at all. I tried so hard to play it, but the notes looked foreign to me and I failed. I tried the other songs and I ended up banging the keys and crying. I vowed never to play it again.

Is this normal? I've been baffled about this for awhile and I've grown envious of others who can play music with ease. I don't just have this problem with piano. One summer, I took a few lessons of guitar and I couldn't play it all... I would like to know how to play instruments, but I can't.... Has this happened to anyone else or is this the cause of a medical problem?