Well, I want to say "I am/was speechless"... I know that you (Turks) use "dilim tutuldu" for such phrases... but my question is: may I use "dilim tutuldum..." for saying "I was speechless"?

"dilim tutuldum" is not correct, because -m should not be there. It literally means "my toungue is stuck" so your tongue, "it" is the subject of this sentence, not "me".

dil = tongue

dilim = my tongue

tutmak = to hold

tutulmak = to be hold (passive voice)

dilim tutuldu = my tongue is hold (I cannot move my tongue, I cannot speak)

There are lots of things about this. I think you are not ready for them yet.

Shortly, this is actually in past tense but as a ´situation change´

it is like ´my tongue has been hold´ (and so I can´t talk NOW)

As it is already past, you cannot make it past again.

There are other forms of past in Turkish. If you are telling a story, you can build the sentence by this form:

dilim tutulmuştu

It has some more explanation which will probably not suitable to write about it long and long.