If this is just a whim be patient, the feeling may pass

. You could try to occasionally attend the local Coptic (Orthodox) church to absorb the spirituality, nothing actually wrong with that.
Of course, you will need to attend your regular parish to meet your Sunday ‘obligation’ as well.
If, after a while, you still feel that this is right for you, there is a way to canonically change rites. You will probably have to meet the most local Coptic Catholic priest (he may not actually be in Turkey, perhaps Lebanon or Israel ??? … ) so you would have to plan a trip. It might be even better to find a monastery in that tradition and associate with it (as an “oblate” or whatever they might call it).
If you can become a long distance sponsor of the Coptic Catholic parish or monastery (wherever it is) this will help you present the case for a canonical transfer. There is still no guarantee that your Latin bishop (or Apostolic Visitator) will agree to the change, however.
It may be that there will be Armenian Catholic, Maronite Catholic or Syriac Catholic churches closer to your residence. In your situation it seems that one needs to be pragmatic. So I advise that you check these out as well.
Read the Patristic literature, if you can get it. There were so many Fathers of the church from the region, in the Greek, Syrian and Egyptian traditions. Do not deny yourself the opportunity to enrich your Faith in this way. This is the joint patrimony of all the Catholic and Orthodox churches, it is your (religious) past and your future!
In any case, all of the Eastern Catholic churches have the LOTH, but it differs a bit from church to church … and yes, it is perfectly alright to use Orthodox texts if that is what is available.