red sore nose tip

hi all,
for about a month i have had pain in my nose, specifically the tip, it was sorr to touvh but as of 2 days ago it has become quite inflamed and angry looking. its gone red and somewhat swollen, the pain is not constant and feels like theres a pulse in my nose, its not excruciating by any means id give it a 4/10 but it is constant and getting worse along with the redness.
ive never had any problems with my nose, ive looked into different possibilities, ive seen that you cant break the tip of your nose, could the cartilage be damaged? ive seen something else about a bacterial infection but i have none of the other symptoms apart from a red nose - from about where it began i did have an injury (i was hit in the nose with a toy(accidentally)), and a couple of days ago i was wacked again (the joys of babysitting lol) , has this possibly flared it up? is it even worth going to the drs because i know there’s practically nothing they can do for a *broken* nose, especially if its just cartillage damade? ill add a photo for reference.
thanks in advance!