Can a sinus infection cause bump on roof of mouth?

Bump on gums: Yes, but it may be a tooth infection, see a dentist for an x-ray asap.

Not likely: The sinus is an open space and when infected should not show any signs of swelling within your mouth. The upper molar teeth all have one root that extends onto your palate (roof of your mouth). If one of these teeth has an advanced abscess, swelling can result. Coincidentally, this same abscess can expand and involve the sinus, so there can be a link but it starts with the tooth.