After being terminated from job, can I still go to a doctor to get med examination of an injury obtained while employed. Workmanscomp claim?

Question Details: While working I developed a discomfort in the palm of my left hand. Gradually , the pain increased. Did not file a claim with company,of fear of being fired. Got terminated anyway, different reason, but now I have difficulty getting a good job, since I can not use my hand to the fullest. Need to see a doctor, but have no knowledge about what my rights are.Do I need to go to doctor to get evaluation and who and how would this to be considered a workmanscomp case? Please advise, need to do something. Thank you Important Notice