About the publicized thing:
It's this paragraph, right?
あぁ隣で同じ方向見つめてる (aa tonari de onaji houkou mitsumete ru)
君と掲げたこの愛に胸を張っている (kimi to kakageta kono ai ni mune wo hatte iru)
I personally translated it as:
You're by my side, looking in the same direction
I'm confident of this love which I hold high with you
(my full translation if you're interested is
here)
"Publicized" is probably the translation of 掲げた (kakageta). It literally means to hold something high (like to hoist a flag, or hold up a prize). In a less literal sense it means to parade something around or show something to everyone (like a company parading a certain slogan).
It's difficult to translate, but she's saying something along the lines of: we're confident in this love and we hold it high for everyone to see.
I'm not sure why the translator used "fills my heart" either. "Mune wo hatte ru" means to feel confident and proud (of something).