If you lived a really good life without doing anything bad or being unhealthy, will you still have problems of some sort?

Yes , for sure , even after doing every thing right , one has to face some thing wrong or adversities , at professional level or personal level or social reason ,

As , by keep doing right and good one can save oneself and one cant ensure - better circumstances around oneself

for example — one can keep oneself fit and healthy diet and exercise , but one cant stop , pollution of air and hence breathing polluted air for his/her entire life

And to understand this , one need to understand -religious philosophies- specially - Hindu Religious philosophy- which has some potential explanation in hand to identify “Why bad thing happens to good people ?”

( Other Religions has -kicked away this basic question of - “why bad things happens to good people “ - by answering it into one line , and that line is —— “God wills it” to turn a God almighty into -malevolent entity”)

This phenomenon is identified in Hindu Religious Philosophy as - “Combined Karma” and for attainment of Moksha or Mukti one is asked to — keep doing - “Jagat Kallyan” ( welfare of entire world and living creatures) so that can reduce ill effects of =Bad Combine karma - of entire world onto one’s life and one cant experience far better life and better results of his/her deeds ,,

For better identification of meaning of Karma , please read this article :-

Morality, Freedom of Will, Self Sacrifice & Law of Karma

By keep choosing -- actions-- with a sense of morality, over just willfulness, one can get away from all karmic debts, even after enjoying life with all its pleasures and plights.

https://discover.hubpages.com/religion-philosophy/Sense-of-Morality-and-Karma

Now after identifying these 3 pillars , (morality ,freedom of will ,self sacrifice) for Karma , there is need to identify types of Karma , which are basically are pf 3 types:-

1st - personal karma ( what person is doing and wishing in current life time — Freedom of will is all bout related to it )

2nd - combined karma -these are combined action of all individuals of society where person is surviving

(for example what so ever wrong /right happening in India , all Indian has to face it , for example Air pollution , or war/Terrorism or Price inflation or Corona Virus pandemic )

3rd -Karmic debt - these are karmic burdens , for which one life time is not enough to complete it

— Story of Karna from Mahabharat

, [1] was all about this =Karmic debt , and he has to choose self sacrifice to end his karmic cycle

And as you were disappointed for - dishonorable life of Karna , I asked you to please go through article , so that I can clarify , my point to you , about karmic cycle, to explain a reason , behind sufferings of Karna

4th - Akarmic Karma —this type of karma where action bring out -no karmic gain or debt is been gained as person involves in karma as mere compulsion or necessity and not as personal will or wish or attachment , here the idea of - Self righteousness (Dharma) comes to surface and one can start entering into Spiritual world , to understand the entire Drama of Existence , by understanding entire - Law of Karma )

Now , after learning some basic ideas of Karma , now coming to the points of discussion- “If you lived a really good life without doing anything bad or being unhealthy, will you still have problems of some sort?”

So better answer for above question is - As one can only have control on - Akarmic Karma , Personal Karma and has no or very limited control on “Combined Karma” ,one cant expect that even after doing every thing right and good -one will never face any thing bad ,,,,,

And that is why “Bad Things Keep Happening with Good people Too “