Hi Elena,
Thal minor can range from silent carrier status with no symptoms to transfusion dependency in rare cases of the dominant thal gene. There has been very little research into the health of thal minors and as a result, most doctors are unaware that it can have symptoms that adversely affect quality of life. In your case, if you do have it, it would be called silent carrier. The main danger here is for future generations so getting a diagnosis is very important. If your cousin has thal trait, then one of his parents absolutely has to also carry the trait, as there is no way to get it other than inheritance. The fact that a relative does have the trait does make it even more necessary for you to determine if you also carry it.
While there has been little research into the effects of thal minor, we have many members who are minors and have repeatedly testified to health conditions that are all very similar. The common thread beyond minor is that the lower the hemoglobin level, the more symptoms that are experienced. You will find very few doctors who will acknowledge that thal minor can affect one's health, but we do hope that patients will also tell their doctors so that doctors can become better informed.