Hi, My Nostrils Are Swollen And I Have Been Bleeding

Hi, my nostrils are swollen and I have been bleeding a bit for the past 2 days.

I have a history of nasal infections.

I had this issue a few weeks back, and it seems to have gone away, but now again.

Not sure if it came back because of a new cat pet.
Also, if this helps, my eyes have been itching for 3 days, but they feel better now.

Just wanted to know if this may require prescripttion.