Problem with cat bite

I was bit on the hand last night by my neighbors 18 yr old cat, who was fretting about her master not being home. The puncture wounds are at on top of my hand by the thumb joint and over about 3 inches. I immediately scrubbed it out, used peroxide and antibiotic ointment. I woke at 330a with pain. Now at 5p, I have a 100 degree temp and it is red and swollen. I have aching all the way up my arm (which freaks me out as I had shoulder surgery on that side a little over a month ago), and feel ill. I have been taking ibuprofen for the achiness. I just squeezed a whole bunch of reddish THICK pus out, soaked it again, medicated it again, and I am wondering if I should go see the urgent care doc. There is a hole where the pus came out and I forced a bunch of antibiotic cream down it. Thoughts anyone?? I really don't want to go to the doc if I don't have to and am thinking that maybe since I got the pus all out it will heal????