Bloodshot eyes without any blurring of vision/ eye discharge may be due to subconjunctival hemorrhage
/ pingeculitis/ inflamed pterygium
And in your case since it is more localized with dilated vessels from it, mostly probably it is either pingeculitis or an inflammed pterygium .
You need not worry in either of these conditions,as it is a localized inflammation of the conjunctival tissue due to allergy/excess heat exposure. Since it is there for more than a week, confirm it with an ophthalmologist after which you may be started on an anti inflammatory eyedrops or a mild steroid
for a faster recovery.
more than a week ,should not be ignored and must be examined at the earliest.
Keep us updated after your checkup. Take care :).