Is "te" the indirect object pronoun of this sentence? If so, why use the indirect object pronoun if the verb is already conjugated?

Is "te" the indirect object pronoun of this sentence? If so, why use the indirect object pronoun if the verb is already conjugated?

Sé cómo te sientes. — I know how you feel.

Is "te" the indirect object pronoun? If so, why do I need "te" if the conjugated verb already indicates "tú"? Doesn't the sentence mean "I know how you feel" without "te"?

Is this a case where the conjugated verb is indicating the indirect object? I thought the conjugation always indicated the direct object (the who or what).

Thank you for any assistance, I am sure the answer is stupidly simple but this is very confusing to me.