I have little egg looking things on the underside of my leaves and my new buds have died without blooming. I'm thinking some type of bug. How can I get rid of them and make my plant healthy again? My leaves also have yellow/brown spots on them.
Likely Mealybugs, and they can be treated with Neem OIl.
Treat the plant weekly.
Here are a few links for you with more information.