Hello Simba! The second sentence isn't very natural. Instead it should be 'I've had more problems than I bargained for'. The sentences have slightly different meanings. In the first one the meaning is 'I've had more problems than I deserve'. We use this phrase to show that we want the situation to change, or we are happy it has changed. It can also be used to show sympathy towards someone else. For example 'I'm glad he got the job. He's had more than his fair share of bad luck recently'. The second sentence means 'I've had more problems than I expected'. For example 'He has had more problems than he bargained for trying to find a job, but I'm glad he found one.' This phrase isn't as sympathetic, and shows that he expected to find a job easily, but didn't. I hope this helps :)

To me, both sentences will send a clear message to the receiver that this person was having quite a lot of problems out of his/her expectation, but things are getting better now. But if you only look solely at the idioms "more than my fair share" it could mean for something negative as well as positive. For example: "I've received more than my fair share of attention here. I enjoyed it though!" Whereas, "more than I bargained" usually mean something unfavorable. Hope I helped! =D

Sentence one makes sense but sentence two doesn't!