HI Anne,
The specialist is right about iron. It should never be taken by thal minors unless a co-existing iron deficient anemia, IDA has been diagnosed by using a group of tests called an iron panel. Iron will not help with the low hemoglobin level of thal minor and can only help when the patient also has IDA. Long term iron supplements when not needed can cause damage to organs and should be avoided.
The symptoms such as coldness and tiredness are common among thal minors. Most minors have an Hb level below normal, so having symptoms of anemia and the corresponding lowered oxygen level should be expected, but most doctors go by the same wrong information that minors don't have symptoms. We do have two studies posted on this site that show the contrary, that minors often do have symptoms. You can't expect much help from doctors concerning thal minor, so you do have to learn what can help. This site is loaded with suggestions and experience of people like yourself, but I will give a few basic suggestions about what may help. Being vegetarian will not cause any problems, and if your diet is based in good nutrition, you may find you feel better. I would suggest that you take a look at our friend Josephine's page,
http://josephinebila.com/ She is a thal major who became vegan and found her health improved dramatically. Although I am not a thal carrier, I am also a vegetarian and have long experience with a veg diet. I also suggest some daily nutrients, chief among them 2-5 mg folic acid, 400 IU natural vitamin E complex, B Complex 100, 500-1000 mg vitamin C and magnesium (for women, calcium and magnesium together in a 2:1 ratio). These are all essential for building red blood cells and maintaining their health. I also cannot under emphasize the importance of having your vitamin D level tested and supplemented if necessary. 50-75% of the people on earth tested for D are deficient and often severely. High doses of D are required to adjust the level to normal (above 30, but 35 should be your minimum goal).
Exercise helps a lot. You have to pace yourself and listen to your body. There is no value to pushing yourself. Do what you can even if just walking and slowly work up to longer periods of exercise. Always understand that your oxygen supply will always be limited by your Hb level, so you should not compare yourself to those without anemia, and also be aware that exercise does help you optimize your oxygen supply.