SPROC that returns unique calculated INT for each call

I'm implementing in my application an event logging system to save some event types from my code, so I've created a table to store the log type and an Incremental ID:

|LogType|CurrentId|
|info   |    1    |
|error  |    5    |

And also a table to save the concrete log record

|LogType|IdLog|Message        |
|info   |1    |Process started|
|error  |5    |some error     |

So, every time I need to save a new record I call a SPROC to calculate the new id for the log type, basically: newId = (currentId + 1). But I am facing an issue with that calculation because if multiple processes calls the SPROC at the same time the "generated Id" is the same, so I'm getting log records with the same Id, and every record must be Id-unique.

This is my SPROC:

ALTER PROCEDURE [dbo].[usp_GetLogId]
    @LogType VARCHAR(MAX)
AS
BEGIN

    SET NOCOUNT ON;

    BEGIN TRANSACTION

    BEGIN TRY

    DECLARE @IdCreated VARCHAR(MAX)

    IF EXISTS (SELECT * FROM TBL_ApplicationLogId WHERE LogType = @LogType)
    BEGIN
        DECLARE @CurrentId BIGINT
        SET @CurrentId = (SELECT CurrentId FROM TBL_ApplicationLogId WHERE LogType = @LogType)

        DECLARE @NewId BIGINT
        SET @NewId = (@CurrentId + 1)

        UPDATE TBL_ApplicationLogId
        SET CurrentId = @NewId
        WHERE LogType = @LogType

        SET @IdCreated = CONVERT(VARCHAR, @NewId)
    END
    ELSE
    BEGIN
        INSERT INTO TBL_ApplicationLogId VALUES(@LogType, 0)

        EXEC @IdCreated = usp_GetLogId @LogType
    END

    END TRY
    BEGIN CATCH

    DECLARE @ErrorMessage NVARCHAR(MAX)
    SET @ErrorMessage = ERROR_MESSAGE()

    IF @@TRANCOUNT > 0
        ROLLBACK TRANSACTION;

    RAISERROR (@ErrorMessage, 16, 1)

    END CATCH

    IF @@TRANCOUNT > 0
        COMMIT TRANSACTION

    SELECT @IdCreated
END

I would appreciate your help to fix the sproc to return an unique id on every call.