Based on your tooth radiograph, there seems to be radiolucency (decay) in the the back most tooth. It has some radiolucency reaching pulpal horn of the tooth indicative of your symptoms. Still a clinical examination needed to be affirmative.
If you are confused about going ahead with RCT, I would suggest to go for direct pulp capping of the tooth under LA.
Basically the decayed exposed part of the pulp horn is lined with a base to protect against any temperature change and on that tooth filling is done. Then this filling is reviewed and followed up over a period of time like one to two weeks. If no pain, you are safe and happy with filling. If pain, you will know you require Root canal treatment for that tooth.
Next Steps
I can understand the confusion you are going through as different people will have different opinions. the best judgement is your symptoms and discomfort. if the pain and sensitivity is too high even to normal water, then surely go with RCT. if there is tenderness on tapping the tooth, again RCT. If not, the above mentioned filling and then follow up can be line of treatment.
Health Tips
don't delay treatment.