as you had unprotected intercourse
the possibility of pregnancy is there, some women can conceive during lactation period also,
your brown spotting
could be hypomenorrhea
means scanty flow due to hormonal disturbance may be because of lactation or anemia due to blood loss in delivery or that could be implantation
feeling of baby moving can be possibly your imagination,
so once you check for pregnancy by doing urine or preferably blood test for pregnancy and ultrasound which will clarify the doubt.