That's why the OR statement is in place. It will evaluate both criteria and match either one. You could put a default date of today's date in the EndDate parameter and the user could change it to something meaningful to them. Change to where clause:
where o.actclass = 'OV' and
(o.apptdate between getdate() and @EndDate or
o.apptdate between getdate() and dateadd("d", @dateInterval, getdate()))
and not exists (select top 1 * from appointments a
where a.person_id = p.person_id and
(convert(datetime, a.appt_date, 101) between getdate() and @EndDate) or
convert(datetime, a.appt_date, 101) between getdate() and dateadd("d", @dateInterval, getdate()))
order by o.apptdate asc
