From the description that you give, these look like enlarged lymph nodes.
These can be enlarged due to infection etc. An armpit lump can be felt enlarged due to shaving, waxing, using a deodarant and other infectious causes.
The throat lumps you mention could be due to some throat infection.
You could wait for a few days, and see if the lymph nodees decrease in size. If not, you would need to consult your doctor and you may need to take an antibiotic course.
For the pain in the neck region, it would be best to take OTC pain relief medications and apply some local analgesic gel. It would also help to do some neck exercises.
Do let us know about the progress.
Hope this helps.