Slightly cheesy penis, painful to pull foreskin back, with end of foreskin slightly puffy and redder than usual and red, white/red patchy on the tip?

Fungal : Fungal balanitis-posthitis is what you are likely describing. It causes a redness and tenderness to the glans penis and swelling to the foreskin making retraction painful and difficult. See your physician or a urologist for a topical cream prescription.

Yeast infection: This sounds like a yeast infection and requires antiyeast cream. The cream can also contain cortisone type medication to combat some of the inflammation but without the antiyeast component in it, the cortisone can worsen the yeast infection.See your physician.