Hi Malshie, I live in Norton which is not far from Tilery, Headlam Street was in Tilery but has been demolished,
The nearest catholic church was St mary's RC on Major Street, which is still there, the catholic school was next door and it was also called St Mary's(I went there myself) Middlesbrough Archives hold the christening records for St Mary's church, if you can give them a ring they will do you a look-up, if you can't let me know and I will book a microfilm machine and do you a look-up
Regards Sheila