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The white dot is on your cornea, the transparent shield in front of eye. This can be due to multiple reasons - a small foreign body like dust particles can cause infection and irritation, beginning of viral infection or a beginning of ulcer.
If you have already tried eye drops and there is no relief, then i would recommend an immediate eye consultation because rarely a simple infection can sometimes become very serious resulting in scarring or decrease in vision.
In the meantime instill lubricating eye drops like refresh tears/systane ultra/optive etc every 2 hours. These are available over the counter
Hope this helps you, do get back for more queries.
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if there is discharge with irritation, then infection has already set in. The infection can be bacterial or viral or a foreign body might be still stuck on your eye. You need a first-hand eye consultation immediately. Kindly do not delay.