Depo injection

Hi girls. I recently went back on the injection (May 21st) whilst on the first day of my last period but I’m still getting the browny discharge like the beginning of a period, can anyone tell me if this is normal or do I need to go back to the doctors. My new partner wanted to have sex this evening but I said no because of this, it’s embarrassing for me to let him see that! What can I do, please help me, I don’t want to push him away just because of this! 😔