Confused newbie (to PG not DB's)

I have setup a database that I am the owner of, and I am trying to setup
constraints and it doesn't seem to be working

Example

- Table: public."Invoice_Header"

-- DROP TABLE public."Invoice_Header";

CREATE TABLE public."Invoice_Header"
(
  "Inv_ID" int4 NOT NULL DEFAULT nextval('public."Invoice
Header_ID_seq"'::text),
  "client_ID" int2 NOT NULL,
  payable_recievable varchar(5),
  "date_CREATED" date,
  "AMOUNT" money,
  amount_paid money,
  date_paid date
) WITH OIDS;

I am trying to make Inv_ID a primary key as follows

alter table Invoice_Header ADD CONSTRAINT PK_inv PRIMARY KEY (Inv_ID)

which runs without error, but nothing changes

this is from psql with PG 7.3.2

any help appreciated