Hi and sorry you had this happen. It is probably best to wear goggles but most dentists don't. You have some low risk of Hepatitis C and HIV of about 0.1% or less. You should be fine for the Hepatitis B. It helps that you rinsed your eye soon after. It is also unknown whether there was blood in the drop that got into your eye. But you have to assume it is possible. At least there is now treatment for Chronic Hepatitis C if that ever occurs and it is cure if you can pay for it for the types that used to be untreatable. So if you want to get tested for HIV get a 4th generation test Now for baseline, in about 30 days then conclusive for HIV 1 &2 at 1 month.
HCV is good to get a baseline now and then 8-12 weeks.
Do you have an employer or do you employ yourself? If you have an employer you should report it immediately. They will send you for testing. If they don't do HIV and HCV you should do it yourself.
It is a very low risk so try if you can not to worry.
Of course if you get any bacterial infection in your eye you can see an eye doctor for that. You would know by redness, swelling or pain in the eye. They can just give you antibiotic eye drops.
Hope this helps.
You could get another booster immediately. That's what my doctor recommended when I talked about possible exposure to Hep B. Because even with all the Hepatitis shots, it's not guranteed that you're protected. So if you know it was possible you were exposed, it doesn't hurt to get one.
Also you should have a complete history of patient's diseases on file for these reasons. You're working in a bloody and liquids field everyday. Why not invest in some really nice high tech good glasses/goggles? Even if you're not getting a splatter, the percentage is high that you have constant exposure to small amounts of blood or fluids.
What I would do is call the patient and ask for a personal medical history. Tell them why. I think that legally anyone with HIV has a right not tell. But I'm not sure what the rules are if someone has been exposed to their blood.
Whatever the case, you should have a blood/pathogen exposure protocol on hand and steps listed on who to call, what to do.
In the hospital after blood/HIV exposure, staff has so and so hours to get treated and get shots.
Best thing to do is to get tested. HIV and Hep B takes 12 weeks (although since you already have the vaccination I wouldn't necessarily worry about Hep B) and Hep C can take up to 6 months for antibodies to appear.