Assalamu Alaykom.
I think it's a blessing if Allah gave you a soft heart and such a level of imaan, may Allah keep you steadfast. I don't think it's a problem.
But if you think it's embarrassing to be overwhelmed with tears in front of people, may be if you prepare yourself emotionnally you can prevent it,
for example if you think that such verse or such idea will make you very emotional, prepare yourself before saying it.
And as I said, it's a blessing so do not try to stop it, especially when you are alone. Actually we all wish to have such a level of faith, but unfortunately sometimes our hearts become hard because of everyday's life, so when such spiritual moments come we should take advantage from it
Allah S.W.T says :
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"They only are the (true) believers whose hearts feel fear when Allah is mentioned, and when revelations of Allah are recited unto them they increase their faith, and who trust in their Lord"
[Al-Anfal : 2].
"Say: Believe therein or believe not, lo! those who were given knowledge before it, when it is read unto them, fall down prostrate on their faces, adoring, (107) Saying: Glory to our Lord! Verily the promise of our Lord must be fulfilled. (108) They fall down on their faces, weeping, and it increaseth humility in them. (109)"
[Al-Israa' : 107-109].
A hadeeth :
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Abu Hurairah (May Allah be pleased with him) reported: Messenger of Allah (PBUH) said, "Seven people Allah will give them His Shade on the Day when there would be no shade but the Shade of His Throne (i.e., on the Day of Resurrection): And they are: a just ruler; a youth who grew up with the worship of Allah; a person whose heart is attached to the mosques, two men who love and meet each other and depart from each other for the sake of Allah; a man whom an extremely beautiful woman seduces (for illicit relation), but he (rejects this offer and) says: `I fear Allah'; a man who gives in charity and conceals it (to such an extent) that the left hand does not know what the right has given; and a man who remembers Allah in solitude and his eyes become tearful".
[Al-Bukhari and Muslim].