Thanks for asking the query,
Painless lump at the roof of the mouth can due to spread of infection from the infected tooth,
bacterial infection in the tooth has lead to abscess
formation that had drained in the palatal area leading to formation of lump.
Moreover the lesion may also be formed due to injury
by food products, cracked tooth.
I suggest you to consult a Dentist
and get examination done and an x-ray done.
Pain near the nostrils can be radiating from the infected tooth.
Take a course of antibiotics and analgesic
Use lukewarm saline gargles 3-4 times a day, use chlorhexidine
mouthwash gargles twice daily.
Hope this helps out.