In reply to Timmd:
Hi Tim,
I am a dentist, can offer some advice.
The 'squishy' lump is likely to be the be a
build up of pus/blood/bacteria as a result of the dead pulp inside the offending tooth- an abcess.
A dental abcess is more painful if pressure builds up with nowhere for it to go, this gives the typical throbbing pain that people don't forget in a hurry!
Draining the abcess is the treatment of choice- this can be done by removing the tooth or by piercing the gum to allow pus to drain- massaging the area will help and rinse with warm salty water.
Antibiotics should be avoided unless absolutely necessary.
Hope this helps- glad you've got arrangements to see you're own dentist and not just leaving things