Can I be allergic to some BC?

Recently I've gotten a new format of BC (the implant in my arm), almost a month ago and I'm noticing that my skin has really been irritating lately itchy and swollen specially my inner thighs and my feet.

I've been monitoring my activities and have not done anything different. I haven't had a period since July.

The worst and most embarrassing thing happened to me today im slowly loosing control of my bladder, one minute I needed to pee the next 10 secs I was wet... omg what is happening to me?

The only thing that comes to mind is the birth control... I'm allergic to cats but I've never had a reaction like this.