It’s very normal, and well done for asking. It’s just, as you said, a lot of emotion going on, which is great if you feel safe, and crying is just a very helpful way of letting out that pressure. It’s really cathartic actually, and if there’s other stresses that are getting to you then this kind of thing can be a safe, controlled way of releasing some of those too.
So don’t be freaked out, keep talking about it, make sure you’re both very comfortable using safewords too and that’ll help you both feel that while you’re getting emotional, it’s all okay.
Try different things too, slaps, spanking, maybe a soft flogger (the elastic ones are a fun stingy starting point) and explore together how various things affect you. There’s more to discover!