From the little context that you include, "I've spent three days since I've become a doctor" is much more natural in English.
author of The Secret Lives of English Verbs
Student or Learner
I heard "I spend three days since I became a doctor" from a cartoon but in my own opinion it should be "I've spent three days since (I've become) a doctor" I'm not sure that is the meaning of since I've become the same as since I became? If it is not the same what are the meanings of these two?
I would suggest that this is correct:
"I've spent three days since I became a doctor", but as competence has said it needs more context to be sure.
bhaisahab could you explain more why you use I became. also could you explain the differences between ....since I've become and .....since I became?
However, many people would use the present perfect in some expressions.
"Since I've become a doctor, I've become more compassionate towards people". This is acceptable because it doesn't refer to the specific time at which the person became a doctor, but to some time or time span since becoming a doctor up until now. But even this can use the simple past, because it means "During the period since I became a doctor..."
Some constructions, such as "Since I've been a doctor ..." are common, because "Since I am/was a doctor" are wrong. "Since I've been a doctor, I've seen many sad cases." But even this can be changed to "Since I became a doctor..."
It's hard to say that [since + present perfect] is wrong, because it's so commonly used.
Others might disagree.
I spent three days in New York.
I have spent 4 hours waiting for this train!
Your sentence needs some additional information, and it is likely that it should be related to what was done, or alternatively information relating to location.
I've spent three days in the local surgery since becoming a doctor
I've spent three days helping patients since becoming a doctor
It is difficult to offer you advice without having more context.
One more question
What if I use (I've become since ......) and (I became since ......), are these both correct or if it's not both correct, can you explain why we use this one?