I realize that it is all done now since you have confessed and been to mass but here are my opinions:
Did you sin? Yes.
My answer: Yes, i did.
Was it a mortal sin? Probably not.
You missed the mass you were planning on attending due to the alarm not going off. No sin or problem there.
Keep in mind that conditions for mortal sin are that you have full control of yourself and that you must knowingly and willingly commit the sin. In your case, I would say that this was compromised. I may be wrong about this but I gather two things. You are rather young (less than 25, maybe even a teenager) and you are somewhat of a new Catholic (I could be totally wrong about this). To me it sounds like you had a difficult choice to make and you had to make it relatively quickly. You thought about and tried to make what you thought in your mind was the right decision. Because of your age and you thinking that you made the right decision, I would say your responsibility in this sin was diminished and therefore it was not a mortal sin.
My answer: I am new as catholic, but old enough to know better. But i had to make a decision yes and asked three times if i could go and it was blatantly refused.
I should have gone anyway, that i realize now.
Did you make the wrong decision? Yes.
My answer: I so do agree, it was wrong.
However, I believe you have learned from it and will know better in the future. You definitly did the right thing by going to confession.
Also as another poster said, any priest who would be annoyed by you going to confession 10 days later, well, I think you need to find a new confessor.
My answer: I have learned from this experience and the priest, not my regular confessor priest was understanding and he told me that many people experience this kind of situation.
There are even places in Norway where catholics cannot attend mass weekly because there are not enough churches or priests. They are in a far else situation than mine.
So i have learned much from this experience and i have spoken directly to the Lord and told him that my choice was wrong.