In the first rakah of fajr I have been saying the tashahhud and for the 2nd rakah. I didn't realise this mistake and now know it's only meant to be said in the 2nd. Will my prayers still be valid as I'm fairly new to praying
According to Ibn Qudamah (12th century CE Hanbali jurist) doing something additional in the prayer that is part of the prayer (such as tashahhud) does not nullify it if it is not intentional, but only requires that one perform two extra prostrations at the end of the prayer to make up for the mistake. These extra prostrations are known as sajdat al-sahwu, and they are considered voluntary, rather than obligatory, by the Shafi`ite and Malikite schools.
From these it appears that your prayers are valid and that there might be nothing more you should do, unless you follow a different school of thought. But I recommend that you ask your local imam, since I couldn’t find any rulings that apply exactly to your situation (adding something extra to a prayer and repeating this mistake long-term).