I'm so sorry you found this little spot of blood on the outer corner of your cat's eye and it's slightly swollen. Because he is an indoor-outdoor cat and has gotten into fights in the past, it's very possible that he had a fight with another cat or 'critter' and sustained a scratch or bite near the outer corner of his eye. There is a lot of bacteria under a cat's claws and in his saliva, so it's important to keep an eye on this area and to have him evaluated in person, asap, by a vet. Once the vet looks at it, it will be treated and antibiotics may be prescribed. I hope your kitty is up to date on all his shots, especially if he goes outside!
For the moment, you can gently clean the area with some Betadine diluted with water, to the color of weak tea, or if you don't want to go out, considering this is so close to his eye, just use some warm water on a cotton ball and see if it continues to bleed. Hopefully, it has stopped. For the swelling and to draw out infection, should there be one, take a regular tea bag, wet it with warm water, squeeze it out and place it on the affected area for about 3-5 minutes, as he'll allow. Do this every few hours. Make sure none of the tea drips into his eye. The tannin in the tea will help draw out infection. You can also apply a thin film of Neosporin ointment on the area after cleaning it and finishing with the tea bag. Keep in mind this is just a temporary measure until you can have him seen by your vet, or if you want to bring him in tonight, an ER vet. Check the inside of his eye to look for any scratches, abrasions, discoloration, difference in pupil size; it's good that his 3rd eyelid is not up, so hopefully, the scratch or bite was just on his skin next to his eye.
It's also possible that he got stung or bitten by an insect or spider or snake, depending on your location, and that is causing his symptoms. If it's not painful to him, try to see his skin through his fur, to see if it is actually a cat scratch, a bite (would look like one or two fang marks), an insect sting--red bump/swollen, a spider bite would look swollen and red), or a snake bite (would look like two fang marks, also).
If you decide not bring him to the ER vet tonight, monitor him carefully and if you notice any unusual symptoms, then, you'll need to bring him in.
I hope all will be well with your furry boy!
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