Scratch On Forearm While Cleaning, Bleeding Inside. Used Peroxide, Antibiotic Cream, Bandage. What Else Should I Do?

I cleaned my oven 2 days ago, and didnt notice that i had gotten a line of easy off oven cleaner on my foearm.It looked like a scratch so i rinsed it off and even scrubbed it with dawn dishwashing liguid to cut the greasy stuff, it appears that there was no scratch rather just a line of cleaner had burned into my skin, after the scrubbing it turned red as if it was bleeding inside, i put peroxcide on it then rinced off, used hibacleanse then put antibiotic cream on it then put a guaze bandage on it, but the area is feeling warm and a little swollen, what else should i do and can that cause a bigger infection.