the difference between mieć and miewać
'Mieć' can be translated as 'to have' or 'to have had' and naturally connects with word like teraz (now), zawsze (always), od wczoraj (since yesterday), od dwóch dni (for two days). It implies that something happens continuously (no matter if only now or a whole year).
Mam ból głowy (I have a headache).
Od tygodnia mam nową prace. (I have had a new job for a week).
'Miewać' can be also translated as 'to have' but it connects with words like 'od czasu do czasu' (from time to time), czasami (sometimes), w deszczowe dni (on rainy days).
It implies that something happens only ocasionally (not necesserilly now, but it has happened already and is expected to happen again).
Czasami miewam trudne zadania do wykonania (I have hard tasks to do sometimes).
W deszczowe dni miewam bóle głowy (On rainy days I happen to have headache).
Hope it helps you a little.