dnd 5e – Can a Monk perform martial arts attacks while using and using a weapon?

I intend to play a monk in the group's next 5e campaign who can grapple with the gripper. I wondered during the confrontation with unarmed attacks of martial arts.

Can a monk attack a single target, attack it with a one-handed weapon, and then make an unarmed attack from that attack?

I'm pretty sure I can do that if my non-gripping hand does not hold a weapon, but I think the rules suggest that I can not do this when my non-gripping hand holds a gun.