Prevod - Engleski-Turski - Don´t say "I love you". Let me feel it!

Is this translation right? "I love you" = "Seni seviyorum" ?

yes

But the translation "Bana beni sevdiğini söyleme, bırak hissedeyim." is right?
There aren't "" and "." and "!"

this translation is true , not matter ..

The translation is correct. The way quotations are done in Turkish is that the quotation is turned into a noun phrase, so that literally it translates as "To me me the-loving-you-did don't say, allow the-feeling-I-do" - Turkish is a very difficult language to learn for this reason!