Can a high tsh level but normal t4 cause hypothyroid symptoms or not?

Maybe: Your symptoms may be from subtle hypothyroidism. Although your T4 is in the normal range, it may be lower than it was. Some people are sensitive to minor variations in t4. On the other hand, the symptoms of hypothyroid can be due to other things. Once you get treated with levothyroxine, you will know.

Yes: Hypothyroidism can be primary - caused by a weak thyroid gland or secondary to other hormonal problems, like a pituitary problem. Or your thyroid can become dysfunctional secondary to high insulin, estrogen or cortisol. If you have functional hypothyroidism, this problem can go undetected by routine screening tests. More extensive testing can often reveal abonormalities. This is very common.