Your red dot in the eyes may be caused by the dryness of the eyes. You could use the eyes drops with anti-inflammation to get rid of the red dot in the eyes. You could also use the warm compress every day to make the symptom of red dot in the eyes get released. You could have a try. In addition, you'd better not eat the spicy food these days which could stimulate your eyes nerves.
It looks like your problem is quite serious according to your words. So, this is likely to be subconjunctival hemorrhage, which is due to conjunctivitis, and that is a popular infection. So you should try to apply some hot compress to that area, and head directly to a hospital. In addition to those efforts, you should get a better diet with more vitamins such as A and E, B. Hope you recover with no time.