The slimy thick stuff you had was cervical mucus plug
. It is this plug which is released when you are heading into labour. Also you say you have contactions and back ache which are all indications that you are progressing into labour. Since you are already 3 cm , you should not be waiting for breaking of your water bag to go to the hospital.
Also dont put any efforts to break your water bag. Water bag if bursts early in labour can lead to infections , chances increasing when labour is prolonged.
Breaking of water does enhance contractions but it s done at a specific time in labour and by a doctor.