Ching,
You may be aware, but OFM has 3 full sets of legs toward it’s front and some (what I’ll call) “proto” legs at the back. I can’t tell if your insect is legless or not. If it’s legless it’s PC. If it has little legs at the front, then it’s OFM.
Obviously your peach has OFM if it is been damage as evidenced by flagged shoots.
If you want to control OFM with the simplest means possible, I’ll try to offer the simplest solution I can think of for you. I can tell you are frustrated trying to sort everything out. You don’t want to spend a ton of time researching. I sense you are saying, “Just give me the name of a product which will work.”
There are many products which would fit this requirement. Some “work” (i.e. kill) OFM better than others.
Probably the easiest available for you (given you have one peach tree) is the new formula of Sevin. It’s called Garden Tech Sevin Insect Killer Concentrate. It’s the Sevin with the active ingredient Zeta Cypermethrin. It’s not the Sevin with the active ingredient carbaryl.
It comes in several different sizes (pint, quart, gallon). I would recommend at least a quart, as one quart of concentrate will only make 8 gallons of spray. A gallon of that concentrate will make 32 gallons of spray.
Mix that in your pump up sprayer. Make sure you’ve not used your pump up sprayer for herbicides. If you have used herbicides in your pump up sprayer, wash your sprayer out thoroughly with soap and water. Then place a 10% solution of household ammonia and water in the sprayer. Shake that solution up and spray a little of the ammonia solution through the nozzle. Then let that sit overnight. Then wash out the ammonia solution thoroughly with clean water. Then you can use your sprayer for insecticide for you peach tree. Spray your peach tree thoroughly up to the point of run-off.
That product should work for you on OFM. However, another component of insect control, is how often to spray. The label of the aforementioned product allows a weekly application (starting at petal fall) with a 14 day pre-harvest interval for peaches.
If you want to be certain to get a peach crop unaffected by OFM, you could spray weekly, as the label allows, stopping 2 weeks prior to harvest. Generally not that many sprays are required.
OFM egg laying comes in waves (generations) with a new wave about once a month. Perfect timing requires traps and degree day models. Some people get by with very few sprays. Others have much higher pest pressure and require more sprays.
There are many homeowner spray guides on this forum in the Guides section and also on the internet, if you want to try to spray less than once per week with your Sevin.