If you have pain or discharge or blurred vision I would leave the contact out and see an ophthalmologist. If the eye feels great, sees normally and everything is OK except for a small bloody red spot on the white of the eye like a small hemorrhage, you might be able to wear your contact but, of course, I am not there to look at you. Use your judgement and if you have any discomfort or pain, or vision loss, see ophthalmologist right away and don't use contact.
MJK MD
This happened to me before. The redness will usually go away in the next few days or so. It is not a good idea to wear your contacts until then. (I know, I know, I totally hate wearing my ugly thick glasses but got to do the right thin). Best of luck!