If you run this:

EXEC sp_help MyTroublesomeTable you'll find five returned recordsets. The second of which details information about the columns within the table. The column Nullable should give you the info you need.

Running EXEC sp_columns MyTroublesomeTable , as its name suggests, focuses purely on the columns in the specified table; returning only one recordset. The columns NULLABLE and IS_NULLABLE could be of interest to you.

Hope this helps, or at least gives you a prod in the right direction.