No, your piercing is not healed. You shouldn't even be taking the jewelry off and putting it back on. Ear lobe piercings take 3-4 months to fully heal. The fact that yours is still bleeding is an obvious clue that it is still healing. Just because it is not painful doesn't mean it's healed. Changing or removing jewelry before it's healed increases risk of infection and increases healing time because you are damaging the healing tissues. Also, having earrings that are not hypoallergenic will affect ANY piercing, healed or not. If you have sensitive skin/ears you need to make sure your earrings are high quality material, such as titanium.
I think a month is plenty of time, I changed my earrings three weeks after I got them pierced and I had no problems. I'm no professional but I say its fine.
