Hi, thank you for the question. There is no medical evidence or medical reason linking drinking cold water/ eating cold food and menstrual cramps. Having said that, sometimes what you experience and what medical evidence and reason says might be different. Everyone's body and mind responds differently to different stimuli. So if you personally notice and experience a correlation between drinking cold water / eating cold food and making your menstrual cramps worse, then do avoid it and drink warm water and take warm food.
Soaking in a warm bath and applying a warm water bottle to your lower abdomen might help ease your menstrual cramps.

Hi @brontosaurus this sounds like a long-standing and persistent condition that needs to be evaluated.

Some variations in period cycles are expected during periods of stress for example, however they shouldn't be less than 21 days or more than 35 days on a regular basis, and there shouldn't be large variations (>2 weeks) between your longer and shorter cycles. These are features that require further assessment and potentially investigations to rule-out possible causes such as thyroid disorder or polycystic ovarian syndrome (PCOS).

You may not have anything to worry about, however given that you have some of those abovementioned features requiring further assessment, I would recommend for your to speak to your parents and/or arrange a review with your doctor for a more detailed conversation about this. 

The best thing to do next is a simple urine pregnancy test at home. If the test is negative, you may wait for another week to see if menstruation starts naturally. If it is still delayed, please repeat the pregnancy test. You may need to see a gynaecologist for a pelvic scan if the period is delayed for more than 2-3 weeks; the appropriate medicine should be given to induce menstrual flow after the scan. If it is indeed an unplanned pregnancy, you may then arrange with the gynaecologist for the appropriate management.