DO NOT use paint thinner.. How long did you leave it to dry before you decide to take it for a ride? Especially in Texas, the surface may dry quick but you must let it dry away from the sun for 24 hours to get the best results. With the heat over there, it's boiling the paint inside out.. Lol it does look like a hot fudge..
Now, Sand it down nicely or even wet sand it until surface smooths down. Clean the surface to remove all oil contents on it. Apply even coats of primers than sand it down nicely again. Afterwards, apply even coats of paint with clear coat to finish it off. Give at least 30-45 minutes drying time between coats. From your pic of "Before" it seems like you are over spraying your paint on the emblem holder. This will cause your emblem holder to take even longer time to dry and if you noticed, the surface is actually creating a "Orange Skin" effect. Again, try to spray nice even coats and let it dry before continuing to spray more coats. BUT this is only if you want the BEST results with rattle cans.
This may be TOO much work for just a emblem holder but it's a good reference for your future painting projects.
Don’t use paint striper dont sand. The method below works a lot better and this is what I do when I don't like the finish on a model car.
Buy some cheap brake fluid and submerge the part in the brake cleaner. After that give the brake fluid a couple of days to do it’s magic (I’d say 3 days). After that wash the part of with a garden hose (you’ll see the paint slide right off) and then run the part under a sink with some dish soap. This process will not damage the plastic one bit.
Also don’t even spray paint/ air brush if it looks like it wants to rain/snow. The moister in the air will cause you to have fish eyes in your finish.