34 year old female has blood pressure around 110/70 but high pulse (90-110) even at rest. Does this indicate heart related problem?

Possibly. The BP is normal but the heart rate is abnormally fast(over 90) at rest. Causes could be overactive thyroid, fever, anxiety, anemia, stimulants like caffeine, alcohol, drugs or cardiac abnormalities. Your physician should examine you and he/she will order the appropriate tests.