While it is absolutely important to up-to-date on routine vaccines before a trip to any country, Myanmar is no exception. So, it is suggested that you visit your health professional at least few weeks before your trip to check whether you need any routine vaccinations or other preventive measures and those with pre-existing health problems, consulting your doctor would be great.
Vaccines like measles-mumps-rubella (MMR) vaccine, diphtheria-tetanus-pertussis vaccine, varicella (chickenpox) vaccine, cholera, Hepatitis A and B and your yearly flu shot are highly recommended. Although hospitals in Yangon match international-standard, the country's health system is quite deprived so, there may be condition of air evacuation to neighbouring countries if needed. Private hospital in Myanmar is expensive and prior to receiving medical treatment here, cash payment is often required. Therefore, it is advisable to have travel health insurance and available funds to cover all possible health cases in Myanmar and repatriation.
There is no risk of yellow fever in Burma. The government of Burma requires proof of yellow fever vaccination only if you are arriving from a country with risk of yellow fever. This does not include the US. If you are traveling from a country other than the US, check this list to see if you may be required to get the yellow fever vaccine: Countries with risk of yellow fever virus (YFV) transmission. While most of the travelers do have safe trip, what you can do is, you can eat and drink safe, prevent insect bites, use sunscreen to avoid any skin rash or allergy, reduce your exposure to germs, maintain personal hygiene, keep away from animals etc to cutback any risk of falling sick and enjoy your trip to the most.