I think I have begun to care about you, but do you feel something toward me? Sincerely, I would like to know. Check when you get home and I want you to tell me the truth.
This is exactly what is written in the source text. Probabil reffers to something to read, I really do not know. The Romanian text does not make any sense, so I have just translated as it is.
When we use the expression "Te uiţi acasă", that means that you have to look in a book or on the Internet or something like that, when you get home. Maybe it reffers to a letter that the person received or something similar. I do not know. I have translated EXACTLY what was written in Romanian. The Romanian phrase does not have too much sense, I really do not know what the user wanted to say by that.
Here is my opinion:"Do you feel something FOR me" and I would also change "Sincerely, I WANT to know" because for "i would like to know" the Romanian version would sound like this "Aş vrea să ştiu"/"mi-ar plăcea să ştiu"(in the original text it's present tense not conditional tense) and for the last phrase i'd say that the person wanted to write "Te mai gândeşti acasă (la asta)"(you think about it home)