Salaah becoming qadha

This morning I was going to wake for fajar and heard the namaz and saw someone else in the bathroom so I closed my eyes and waited. I didn't realise that I fell asleep and when I got back up it was still dark so I rushed to the bathroom to make wudhu. I am a very doubtful person so making wudhu takes some time but I am trying to get better and did it as fast as I could. When I came back I looked outside and it was still a dark blue and there was little yellow in the far back so I quickly started praying. I didn't think it was that late as fajar happens around 6. I thought it might be 6:30 at the latest but after I prayed 2 sunnats I checked my phone and it was almost 7. So I finished my namaaz. I know it is bad to delay prayer and I didn't mean to. I am so worried I might have prayed in the forbidden time but I remember reading that if you didn't mean to delay fajar prayer you can pray as soon as you remember or wake up so did I do the wrong thing? How do I fix this?