So when I was about thirteen and I had already seen my menstruation I was singing this song and it cursed gods name and I sang along. I didn't mean anything by it. But I felt so bad I repented and made shahada. Up till this day I still ask for forgiveness and make my shahada. Does this make me a non believer?
To leave Islam and become a disbeliever you need to do this intentionally which neither seems to be the case when you where 13 nor now as you still feel bad about it. And even if you did something like that intentionally one must check whether you have been doing this to save your life or by mistake, if so you are excused, but repenting sincerely would be the best.
Allah the almighty says:
Whoever disbelieves in Allah after his belief... except for one who is forced [to renounce his religion] while his heart is secure in faith. But those who [willingly] open their breasts to disbelief, upon them is wrath from Allah , and for them is a great punishment; (16:106)
So basically you should leave your worries and try to be a good Muslim.
The Quran declares:
Say: "O my Servants who have transgressed against their souls! Despair not of the Mercy of Allah: for Allah forgives all sins: for He is Oft-Forgiving, Most Merciful. — Quran, Sura 39 (Az-Zumar), ayah 53
Allah is the forgiver. If you have sinned ask him for forgiveness and repent he will surely forgive you.
Allah's apostle said, "Every son of Adam sins, the best of the sinners are those who repent."
— Sunan al-Tirmidhi,Hadith no. 2499