Unable to scroll ListView even with ScrollPhysics

I have a screen where I need to search for a term from the Appbar, and the area below shows a Card with selections from the displayed list, and the area below that will show all the results returned, within a scrollable list.

The problem is that although the items returned are placed in a ListView.builder and ScrollPhysics is on, the list is not scrollable. If I click on the Card and try to drag, it scrolls for a bit. But one cannot drag by clicking on the list, or items in it.

import '...';

class DiagnosisAdd extends StatefulWidget {
  @override
  _DiagnosisAddState createState() => _DiagnosisAddState();
}

class _DiagnosisAddState extends State<DiagnosisAdd> {
  TextField searchBar;
  TextEditingController searchTextController;
  Network connection;
  List<ICDCode> DiagnosisList;
  List<ICDCode> selectedDiagnoses;

  @override
  void initState() {
    connection = Network();
    DiagnosisList = [];
    selectedDiagnoses = [];
    // searchBar = A widget
    super.initState();
  }

  @override
  Widget build(BuildContext context) {
    return Scaffold(
      appBar: AppBar(
        title: searchBar,
      ),
      body: ListView(
        physics: AlwaysScrollableScrollPhysics(),
        shrinkWrap: true,
        children: [
          Card(
            child: ListTile(
              title: Text("Selected Diagnoses"),
              subtitle: Wrap(
                children: List.generate(
                  selectedDiagnoses.length,
                  (index) => Text(selectedDiagnoses[index].disease),
                  growable: true,
                ),
              ),
            ),
          ),
          ListView.builder(
            physics: AlwaysScrollableScrollPhysics(),
            shrinkWrap: true,
            itemCount: DiagnosisList.length,
            itemBuilder: (BuildContext context, int position) {
              ICDCode codeDiagnosis = DiagnosisList[position];
              return RaisedButton(
                  child:
                      Text('${codeDiagnosis.code}, ${codeDiagnosis.disease}'),
                  onPressed: () {});
            },
          )
        ],
      ),
    );
  }

  Future searchDiagnosis(String text) async {
    if (text.length < 3) {
      return false;
    }
    var response = await connection.searchICDbyDisease(
      searchString: text,
    );
    final jsonResponse = await json.decode(response);
    List<ICDCode> diagnosis_list =
        await jsonResponse.map<ICDCode>((i) => ICDCode.fromJson(i)).toList();
    setState(() {
      DiagnosisList = diagnosis_list;
    });
  }
}