It might be that these are hormonally based headaches that are exacerbated by stress? She is of that age where the effects of hormones can kick in. You could try some light taping to unload or support more the mid thoracic spine rather than the traps which might aggravate her if taped. Focus on the ball and the game is likely to be the reason she has no headaches when playing handball but I would also note that she would be getting a lot of neck 'whip-lashing' type movements being a goalie.

In relation to the biochemistry being involved you could look to the diet and possible supplementation to try to see if it makes any difference to the severity of her symptoms. I would say though that this needs to be preventative as often taking something once a headache is in full swing is not likely to help.

It is also interesting if she does take simple over the counter medications like paracetamol and neurofen plus (with the codeine) to see if either have an effect on the symptoms. This can help add weight to a pathway that the drugs are having an effect on.

Perhaps one last non-musculoskeletal thing to take a look at would be the eyes. If she has a little eye strain, especially with kids and computers then this too could be a contributory factor. Let us know how you get on as teenage headaches can be very difficult to route out the actual cause.