Organic milk cannot contain additional hormones other than those produced by the cow herself.
The website
waswiressen.de is supported by the German government and states the following:
Genau wie in der konventionellen Tierhaltung dürfen in der ökologischen Tierhaltung keine antibiotischen Leistungsförderer im Tierfutter zur Verbesserung der tierischen Leistungen eingesetzt werden. Hormone und Antibiotika dürfen in der ökologischen sowie der konventionellen Tierhaltung nur im Rahmen einer tiermedizinischen Behandlung, also bei Krankheit verabreicht werden. In der konventionellen Milchviehhaltung ist allerdings der Einsatz von Hormonen zulässig, um zum Beispiel den Zeitpunkt der Besamung und damit den Kalbetermin zu beeinflussen (Brunstsynchronisation, Embryotransfer).
As in non-organic farming, no antibiotics may be used to increase yield. Hormones and antibiotics may be used in organic and inorganic farming only as part of a vetinary treatment, i.e. to treat disease. In inorganic milk farming, hormones are permissable at insemination and to influence the time of birth (season synchronisation, embryo transfer).
This is however unusual due to the costs involved. And the milk from sick cows shouldn't come into the food chain.
While there is EU-wide organic labelling in place since the start of this year, many German organic groups have standards higher than the EU ones. Here's some of the groups to look out for: Demeter, Bioland, Biokreis, Naturland, GÄA, Ecoland, Ecovin and Biopark.
Whether giving cow's milk at all is wise, I'm not sure but am sure someone will advise on that one or have a chat to your doctor.