Hi
@Louiser, as far as I'm aware, the type of injection usually used to numb a lower front tooth is typically quite easy on patients. Also, again as far as I know, your tongue won't go numb (though your lower lip may go numb and tingly for a little while). Remember that it will wear off pretty quickly in most people. If you can find something to take your mind off things while waiting for it to wear off, like playing a mindless game on your phone or watching TV, that might help pass the time. I'm not a dentist, so if you want a more definitive answer about numbing a front bottom tooth, you could post in the "Ask a Dentist" section

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Please do make sure you tell your dentist about your concerns beforehand! That way, they can make sure you feel as little as possible, for example by using numbing gel and choosing where and how to give the local for minimum discomfort. They can help you much better if they're aware of your concerns.
Regarding your fear of dry socket - have you experienced dry socket before, or is it just something you've come across online? It's not really all that common and even when it happens, there are simple ways of alleviating it (your dentist can pop in a medicated paste which almost instantly helps the pain).
Did you manage to get an emergency appointment?