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Hi! I have two decades of ophthalmology experience. I'm online and happy to answer your question today.
It is very unlikely that anything from the squashed black ant, even if it did get in your eye, would cause any problems.
For the irritation I suggest you use cold compresses and frequent artificial tears. If your eye is bothering you in 24 hours then you should consult with an ophthalmologist.
There is no over the counter antibiotics available to use in your eyes. Does this make sense to you?
That is probably not a sign of infection but rather dryness and irritation. The good news? From what you have posted here today I believe you will be fine. You might also try scrubbing your eyelids to get rid of any foreign substance.
I like to use baby shampoo for lid scrubs. In the shower, place the shampoo on your index fingers, close your eyes, raise your eyebrows (to stretch the skin on your eyelids) and scrub back and forth along your eyelashes for 3 to 5 minutes.
Does this make sense? I hope this information was helpful for you.
Thanks in advance