A pilot on final approach to a non-towered airport reported an NMAC when they initiated a go-around and preceding traffic made a touch and go and climbed into their path.

Narrative

Had announced myself on CTAF for the straight in on Runway XX. Aircraft on the downwind asked how far I was; I stated 5 miles. At approximately 2.4 from Runway XX; aircraft appear in front of me from my left and entered final on an unstable approach. I reduced power and increased flaps to give spacing. They continued down to the runway; and as I was approaching the aircraft was still on the ground. In order to prevent a runway incursion; I called for the go around and announced on the CTAF. I started to proceed on runway heading starting my climb. As I was climbing; I noticed on the MFD (Multi-Function Flight Display) that the aircraft was performing a touch and go climbing right underneath me. In order to make sure that they didn't climb into me; I evaded by contacting CTAF and calling early crosswind Runway XX. There as I was completing my turn; I saw there was another aircraft starting to enter the downwind from the north I did not initially notice it as it blended in with the haze. I was approximately 800 MSL and went under them and headed towards the water towers to give spacing for the aircraft as I was doing that; I'm not sure if it was the same aircraft or a different aircraft that was coming on the downwind from the north; so instead of making the standard right hand tear drop into the downwind; I performed a left 180 and got in between the aircraft staggered to the west a little bit from standard pattern. I then called CTAF and announced that I will be extending my downwind for Runway XX in order to give spacing to the aircraft landing. After this; I safely landed the aircraft and pulled off the runway and secured the aircraft. I think this is a case of lack of situational awareness on the aircraft that came in front of me and then performed a touch and go. For me too it was reactionary for me to turn towards the pattern downwind as I didn't have time to consider whether or not I could depart to the east as time was a factor. Looking back at the event; I kind of wish that I spent the 5 seconds to check if the east was clear; however I am still concerned that this may have caused an incident if I did not react quickly enough.