Is it normal to have a bump, with white stuff inside after a month of mole removal. (photos)

No, I don't recommend popping this. I recommend following up with your cosmetic dermatologist for a formal evaluation and after care. I recommend Silagen + Bioshield to promote healing. Any scarring can be improved with lasers and microneedling/prp. See an expert. Best, Dr. Emer

Dear Melisa,
It is very hard to see exactly what is going on your pictures.
I would advise making an appointment to see your Plastic surgeon/dermatologist as soon as possible for clinical evaluation. 
It may be a recurrence of the mole, especially if shaved off, could be a sticth grannuloma, or could and most likely is a hypertrophic or keloid scar forming. If it is the latter then I advise moisturising 2-3x per day for 3 months, the application 1-2x daily of silgel (or an equivalent silicone gel) as well as firm massage of the scar, rather like kneading dough, 2-3x daily for 3 months using your index finger. I would also advocate sun block SPF50 daily for two years.
Wishing you all the best.
Marcus