Hi there, I've experienced this for 3 years now and they come and go many times through the year. I get them quite a lot, they are nicknamed tonsil stones and I find I get them more when Im stressed.
They are harmless but quite annoying and can leave a horrible taste in the back of your throat. They can be quite difficult to remove yourself if you have a sensitive gag reflex, but if youre like me then you'l have no trouble.
They are easy to remove with cotton wool buds, just shine a torch down your throat and apply pressure where you can see them and they just pop out. There are many holes in tonsils so can be tricky at times. Just make sure you brush your teeth really well and more importantly the back of your tongue. Because these "tonsil stones" are built up of bacteria. Hope I've helped.
Oral warts are rare, but if you are concerned see a doctor for a diagnosis.
The bump could be anything, such as normal skin or Tonsilloliths.