When I first started having sex, I was in a committed relationship much like yours. I was on the pill and took it consistently, despite this, I was always worried that I would become preganant.
As the pill has a pill free week where you bleed it was enough for me the first 2 months to convince me that I wasn't pregnant, but then I began to think about it more and the fact that it's just a withdrawal bleed and not a real period - every month for about four months I would take a pregnancy test once a month to put my mind at ease (drove my boyfriend nuts) ... I then began to mellow out a bit and started taking a pregnancy test once every 3-4 months and then after a while I stopped. In hindsight I can see how daft I was - I would have known if I was pregnant, I know my body and would have recognized that something wasn't right.
Long story short .. how you're feeling is completely normal in my opinion. There is a tiny risk with all contraception, nothing is 100% but yes you'll be ok with condoms .. you mentioned that the pill messed your body up when you first tried it, and you mentioned you are aware of the morning after pill if necessary. My experiences using the morning after pill were AWFUL - I bled for 3 months straight and was exhausted all the time (all girls experience different things). If you are concerned that a condom alone isn't enough then I would double up on contraception and use a condom and the pill.. there are so many different types of pill you are bound to find one suitable for you. It's all trial and error.
I understand you don't want your mum to find out- going to the doctors is all confidential so she need not know. If you want to tell her without her knowing you're having sex, could you not say that you wanted to try it again for your heavy periods or possibly use spots as an excuse .. the pill balances out your hormones and can improve your complexion.
Don't worry, as long as you're safe you'll be fine. I know it's easier said than done, but for me, looking back on how I acted .. I was just insane!