疼痛 means physical pain, but it is very formal, and usually used in medical speak. This is also similar to 痛楚, which is also too formal for casual conversation.
For example: 肌肉疼痛是感冒病徵。 ~Muscle pain/aches is a flu symptom.
The words 疼 and 痛 are usually used in solidarity, in Mandarin and Cantonese respectively.
For example: (In Mandarin) 我肚子疼。(In Cantonese) 我肚痛。 ~I have a stomachache.
On the contrary, 痛苦 means pain in general. It could still be physical, but usually mental or even metaphorical.
For example: 生產的過程很痛苦。 ~Giving birth is painful.
Bad example: 他看來很痛苦。is as vague as "It looks like he is in pain". It could be physical or mental, and depends on the context.
Another example: 學習中文很痛苦。 ~Learning Chinese is painful. (Based on true experience)