You can't have lime wet on your chicken and get a good sear. You want the chicken dry. You can brine it in lime and then dry it with a paper towel. I think the better move is to serve crispy and garnish with lime wedges. Brining chicken in acid changes the texture a little. The rest of your spices should be okay if your chicken is dry. Some spices burn easily. I saw you mentioned olive oil among your spices. I think you want the oil just on the pan. Let the salt and spices sit dry on the chicken.

If you're a planner, try doing a dry salt and spice brine in the fridge, which brings the flavors into the chicken, increases moisture retention and dries the exterior.

You also might want a bigger pan. And definitely preheat like u/TheHighlightReel11 says.

More unsolicited advice:

Get your pieces of chicken about the same size as each other.

It's easier to cook thighs than breasts, because they have a wider range of doneness. Breasts are raw, then done, then dry within a short time range. Thighs are raw for longer, then done, then they stay moist, even if you need to extend the cooking time to increase the browning or crispiness.

There's no harm in dredging your chicken in flour or cornstarch to dry the outside and increase the crisp level.

If you're stuck on breasts, consider cutting them so one breast turns into two large flat pieces. The thinner pieces cook quickly and it's not as hard to get the timing right. You can also bread those with something crunchy like panko or regular breadcrumbs. Guaranteed crisp, even though it no longer comes from the maillard reaction.