Is thyroid problem possible with normal tsh?

Yes. Most common situation would be low thyroid hormone level, 'normal' tsh, which suggests a pituitary problem.
Yes. First, the 'normal' level is a statistical not a clinical determination. Many people will have symptoms when their thyroid test is in the lower part of the normal range and will benefit from treatment. Unfortunately, older thyroid tests were not as precise as the present 3rd generation test and we were formally taught that we could not diagnose mild hypothyroidism. This is no longer true.

Related Questions

Can you have thyroid problems and normal TSH levels?

Yes. Much depends on the details of the underlying thyroid condition and the type of thyroid testing done. Usually a test called a free T4 can be useful.

Is it normal TSH level, but enlarged thyroid what's the problem?

Goiter. There are many causes of a goiter. The normal TSH suggests the thyroid is making enough thyroid hormone, it just has to get bigger to do this. Check with your endocrinologist. An ultrasound may be a good idea to check for nodules.

Is it possible to have normal tsh, ft4 and t3, (liothyronine) but still to have thyroid problems?

Unlikely. There should be at least some abnormality with one of those labs. Unless youre on a thyroid replacement already.
Yes. You can be hypothyroid due to "tissue resistance" or "receptor insensitivty". Ie--where the thyroid hormone levels and TSH are normal (as the pituitary is still susceptible to negative feedback) but the peripheral "end organ" tissues or receptors do not respond normally to the tropic effects of thyroid hormone.

Normal tsh, free T3 (liothyronine) and 4. Anti thyroglobulin of 0.65, can I have a thyroid problem?

Yes, but. You can but the problem isn't one of over production or under production of thyroid hormone.
Not a functional one. Your thyroid appears to be functioning normally, although you could still have a structural thyroid problem such as a nodule that does not affect the function. You doc should be able to tell you.
Thyroid antibodies? Thyroglobulin isn't helpful here. Anti-thyroid antibodies would be helpful in determining whether hashimoto's thyroiditis is present, which could ultimately affect thyroid function. With normal TSH and ft4 thyroid function is normal right now.
Maybe. With normal tsh, t4, and t3, (liothyronine) your thyroid appears to be functioning normally. But auto-immune thyroid disease can also cause the whole thyroid to enlarge forming a goiter, or specific areas to enlarge, forming nodules. But a lack of problems now doesn't mean you will always be normal. If 0.65 is high for the lab where you were tested, you may develop thyroid problems in the future.