After the salicylic acid slip into your eyes, you should stay calm and rinse your eyes immediately. However, it is harmful to rinse your eyes with tap water. You can buy saline for contact lenses in drug store and use it to flush the remaining of the salicylic acid out. It usually takes one to two days for you to recover. During this time, you can apply high-quality over the counter eye drop to your eyes several times a day. This will lubricate your eyes. If you still suffer from redness, itchiness or overall discomfort in eyes after this period, you must see an oculist.
You say a bit of salicylic acid, so I am sure your eyes won't get hurt as long as flush away the acid in your eyes in time. Rinse your eyes for 15 minutes or more, damage won't be done. If you have red eyes, itchiness, sting or pain after rinshing, you need to see a doctor.
Well, first, in my opinion, you do not need to worry about it too much, for it can be fine. Of course, the first step you should do is to wash your eyes with plenty of pure water. In that way, it will just wash the acids out of your eyes. So that your eyes will not be infected by it, or it can be dangerous. As we know that it will just make your eyes red, burning, itchy in some degree. And then, of course, you have some ice under your eyes too. Ice can just relieve your situation too. By the way, having some eye drops can be perfect. Anyway, just be careful about it.