Brother this matter is always brought up and the answer is always the same. Check here:
http://islamqa.com/en/ref/83035
http://islamqa.com/en/ref/45918
The bottom line is, you only do it if it is necessary, and then you only do the minimum that is required. If you have a job that you must get health insurance for, then that is what you must do otherwise you would be jobless. You cannot drive a car without insurance because it is illegal, yet everyone needs a vehicle for transportation.
To free your self of sin and guilt, ask yourself "is this something that I cannot survive without?" if the answer is yes then it is a necessity, so you do what you have to. Just like eating haraam meat such as pork or ham, if that is your only option then you use it lest you die.
Outside of mandatory insurance, it is all on your strength of Imaan. If you work hard to improve your relationship with Allaah, then you will understand the hadith of the prophet Mohammad (SAAWS):
uhaib reported that Allah's Messenger (may peace be upon him) said: Strange are the ways of a believer for there is good in every affair of his and this is not the case with anyone else except in the case of a believer for if he has an occasion to feel delight, he thanks (God), thus there is a good for him in it, and if he gets into trouble and shows resignation (and endures it patiently), there is a good for him in it.
Strengthen your faith, rely only on Allaah and not anyone else and you will find that you need nothing or no one else. Musa 3alayhi Assalaam, he stood in front of the ocean, and he had no idea what was going to happen. How on earth were they to get out of this situation? The enemy is at your back and in front of you is the vast ocean. Can any human being get out of such a situation? Then the people with him said, "Oh Musa, we are definitely not going to survive!", and that is when Musa said:
And when the two companies saw one another, the companions of Moses said, "Indeed, we are to be overtaken!"
[Moses] said, "No! Indeed, with me is my Lord; He will guide me."
http://islam.thetruecall.com/module...to&gotoparam=26:61-62&at[]=999&at[]=50&at[]=5
Do not doubt Allaah's ability, and do not rely on those who cannot give you what they do not possess.
And if you are Imaan is not strong enough for you, then you do what you will, but surely you will pay for any sins that you commit, either in this life with distress, loss of wealth, discomfort, or punishment in the hereafter.
And Allaah knows best.