The most common causes of headache with nose bleed are anemia
and high blood pressure
and in some cases head injury
may be a fault instead.I think in your condition the cause may be anemia so once have a complete blood count
done and also first rule out if you have any head injury recently.If anemia is the cause then it is ok and by treating anemia by zinc and iron your symptoms will reduce.And the shakey feeling may be due to weakness.If you are diagnosed with sinus infection as in that too the symptoms will be the same antibiotic treatment is sufficient for mild cases.Thank you.