You might have something that is resistant to the antibiotic you took. Warm soaks to the area might help soften things and bring them to a head if it's infected. If you start seeing red streaks travelling from the wound, you need to go to the ER or urgent care right away. You should probably see a doctor and see if they can swab it to see what bacteria you have there.
As mentioned, do not be peeling off a scab. If there is redness and infection, you may require intravenous antibiotics and a stay in the hospital. Get a consult from an infection control expert at a teaching hospital. These infections do not get better. Deep infections may require surgical excision as well as antibiotics.
No you should not be peeling off any scab. The scab will fall off on its own when the underlying flesh has formed new skin under the scab.
Every time you peel off a scab and the wound it not healed underneath, you will cause it to bleed. This is normal. A new scab will then form and the healing process will be going on underneath the scab.
As you have just finished an antibiotic, I imagine that the fall happend about a week ago, in which case this is not long enough for your wound to have healed under the scab. It can take weeks, depending on how quickly your body heals.
With a 5 inch gouge, I am surprised that you did not have any stitches.
If you have a concern that the infection has not cleared up after taking the antibiotics, you really need to see the doctor again for a re evaluation.
Hope you get on alright.