My eyes - both my eyes - simply welled up with tears.
I was just moved to tears by (the concert/the music/the performance).
I was so moved by the performance (concert/music) that my eyes welled up with tears.
「目頭」= the corner of my eye/the inner corner of my eye
「ただただ」= simply/nothing but/just
「目頭が厚くなる」=eyes filled with tears / eyes welled up
原文を直訳すると少し不自然な英語になります。↓
My eyes - both my eyes - simply welled up with tears.
もっと自然な表現はこちら:
I was just moved to tears by (the concert/the music/the performance).
I was so moved by the performance (concert/music) that my eyes welled up with tears.