The years between 12 and 16 are years when the hormones are on the move and not unusual to have problems with masturbation and sins against purity.
Here is what The Catholic Catechism says about mortal sin:
scborromeo.org/ccc/p3s1c1a8.htm#1859
1860 Unintentional ignorance can diminish or even remove the imputability of a grave offense. But no one is deemed to be ignorant of the principles of the moral law, which are written in the conscience of every man. The promptings of feelings and passions can also diminish the voluntary and free character of the offense, as can external pressures or pathological disorders. Sin committed through malice, by deliberate choice of evil, is the gravest.
In other words, the urges of your feelings and passions at a time when hormones are very active may well diminish your freedom to fully consent and mortal sin requires three conditions at the actual time of the offence:
Grave matter
Full knowledge
Full consent (the urgings of your feelings and passions between 12 and 16yrs may preclude full consent - but you would need to speak to a priest about this)
If you have confessed your failures in Confession, then be assured that God has not only forgiven, He has completely forgotten your offenses and returned you to that state of Grace that existed before they were committed. I would think it not at all an unusual problem for a male between 12 and 16, perhaps not for a female either. Your Post does communicate heartfelt sorrow and God would never ever reject such a contrite heart “My eyes are drawn to the humble and contrite heart”:
Psalm 33 "
[19] The Lord is nigh unto them that are of a contrite heart: and he will save the humble of spirit.
[20] Many are the afflictions of the just; but out of them all will the Lord deliver them. "
Isaias (Isaiah) 66:2 “My hand made all these things, and all these things were made, saith the Lord. But to whom shall I have respect, but to him that is poor and little, and of a contrite spirit, and that trembleth at my words?”
Reading your post, it sounds to me that your actual problem is forgiving yourself and you are projecting this on to God and thinking he is having problems forgiving you too. Not so and especially if you are going to regular Confession.
You do not say if your problems have now ceased, how old you now are, nor how far in the past they may be. Go regularly to Confession and keep up that daily rosary and ask Our Lady, Queen of Holy Purity, to guide, guard and help you. When you go to Confession, speak to Father about a call to the priesthood.
The long and short of it all is that you would not be rejected I should not think because you had sexual problems between 12 and 16 years. I would think, however, that any vocation director would expect that your problems were past tense for at least two or three years - and I tend to doubt (I may be wrong) that you would not be considered for the seminary nor a noviciate until at least in your low to mid twenties although diocesan requirements for the seminary and religious orders for their noviciate do vary.
The most important step you can take is to speak to a priest about a possible call to the priesthood - either in Confession or make an appointment to speak with him. Catholic discussion sites can be very helpful, they can also be discouraging, and are never the best and most reliable source to approach, which in spiritual matters is a spiritual director or a priest. I think you have a spiritual problem at the core of things and this is forgiving yourself and also to understand and embrace, to be praising and thankful for, that God forgives the contrite and especially if coupled with Confession.
God bless you and continue to hold you ever close as He does - TS
