Can sensodyne toothpaste really work?

Yes. Try it ; see. I personally use it ; it works. Recommend it to my patients all the time.
Sensodyne work? Yes, absolutely. But if you have a persistently temperature sensitive tooth, try this. Just after brushing your teeth before bedtime take a little, just alittle sensodyne paste onto a swab, paint that sensitive tooth area at the gum line. Spit out too much paste if you have done so. At night you mouth makes very little saliva. So that concentrated paste is absorbed into the tooth fortifying it.
Yes. Sensodyne can be effective in reducing sensitivity in teeth due to gum recession. It will not help decayed or broken teeth. If your try sensodyne and it does not help you after 2 weeks then you should see a dentist and find out what exactly is going on.
Depends. For sensitivity in teeth with gum recession, works well. For teeth with untreated decay, wrong approach. Have to treat the decay for resolution of symptoms.