Hello there, so as the title suggests this is my first post

So my question here is, and iv been trying to figure out all day, is can I become a Teacher if I have done the LCA and not the traditional Leaving Cert?
Iv always wanted to be a teacher, pretty much all my family is made out of teachers so i guess its only normal for me to want to be one so bad.
I completed my LCA with a 74% Merit. (10% off a distinction -_-) Iv been searching and googling all day and this is what iv found out so far:
I can go to GTI (Galway Technical Institute) to do a PLC in Applied Social Studies then if I receive and ONLY if i receive a distinction in 5 or more modules I can progress to do a BA in Arts.
But here's the question I have: If I successfully complete my Arts Degree, can i progress to do a Teaching Diploma? As I understand you need a certain level of Maths in the normal Leaving Cert to apply, but I didnt the Leaving Cert Applied... So does this mean I can't apply for my Teaching Diploma unless I go back and do the normal Leaving Cert?
Head is messed up been searching all day and not one answer. Thanks in advance!