Transaction On Stored Precedures

Hi all
question regarding how transactions work in SQL Server...

stored procedure below that generates unique IDs for messages we
send to the backend It looks like sometimes, the number generated is
identical for a messages that were sent simultaneously. Since this
seems like a concurrency issue, am I correct in thinking that using
SQL
transactions within the stored procedure code will solve this problem?

The stored procedure is outlined below, the code in red is what I
think should go in to solve the concurrency problem.

CREATE PROCEDURE [dbo].[praCCGetNewCDMIndex]
@newdate int
AS

SET NOCOUNT ON

DECLARE @lastdate int
DECLARE @lastindex int
DECLARE @newindex int

BEGIN TRAN CDMIndex

SELECT @lastdate = N_JULIANDATE FROM tbl_CC_CDMIndexes
SELECT @lastindex = N_INDEX FROM tbl_CC_CDMIndexes
IF @lastdate = @newdate
SET @newindex = @lastindex + 1
ELSE
SET @newindex = 1

UPDATE tbl_CC_CDMIndexes
SET N_JULIANDATE = @newdate,
N_INDEX = @newindex
SELECT N_INDEX FROM tbl_CC_CDMIndexes

COMMIT TRAN CDMIndex

SET NOCOUNT OFF
GO