As far as I know the only way is to do NOESY and Coesy protein NMR if your protein is rather small. Exchange with deuterium shoeld give you an idea of hydrogen bonds.
As suggested, NOESY and proton-deuterium exchange experiments will help you estimate hydrogen bond strengths.
A 34 KDa protein is at the limit for solution NMR studies. If the spectral assignment of your protein-of-interest is not already available, then assigning it will be challenging due to larger size. You may have to make deuterated sample with 15N and 13C labels. Hope this gives you some idea.
Possibly differential scanning calorimetry (eventually differential scanning fluorimetry) or properly designed isothermal titration calorimetry experiment can give you some insight in to the strength of bonds in your protein.