Would a numbing injection in the front upper gum make the gum swell?

injection of anesthetic solution in to tissues will cause some swelling. However this is short term and should go away quickly If your gum is still swollen day after , Have the site evaluated , to make sure impression material or dental cement lodged under the gum is not the cause of your swelling. Also Have the fit of new denture evaluated.

The amount of
swelling at an injection site is very minimal, and should not affect the
appearance of your implant supported denture. However, if you feel like there
is some open area in this location, your dentist can add material in the
denture to help re-line it and close up the open space between the denture and
your gum tissue. Keep in mind however, that you want to have a certain amount
of space in order to clean under the prosthesis each day.

but it's normal , it's swollen this will go away in 2 to 3 days you can have ice to help it go away.

It sounds like you have an implant retained overdenture. These generally are very retentive and should not rock during normal chewing. If the denture you have now is the permanent denture and has been attached to the implants, you should return to the dentist for a followup. An implant overdenture can easily be adjusted to achieve better comfort and bite. It can also be relined or have the locator buttons replaced to increase the amount of retention and stability.