I bet it's a calcium deposit. I had one for years. It ws hard, but it looked like a pimple kinda. I kept picking one day with a needle and this hard rock came out. I later found out what it was. Put hydrogon peroxide on it after you pick. it will bubble up.
If the small white dot is painful or irritating, then it is most likely a canker sore (not the same thing as a cold sore). Canker sores one of those wierd things that some people get and some don't and no one really knows why they occur. I get one about once a year and my doctor told me sometimes that can be brought on by stress, either physical or mental stress. They are painful, but no serious threat to anything. You can find over the counter gels / creams or things like anbesol to take to numb the pain a little. it will go away on it's own in a few days.