Hello!!
COMEDK UGET provides admission to all eligible candidates in the participating engineering institutes located in Karnataka. The examination of COMEDK UGET acts as an alternative for engineering admissions in Karnataka after the state examination.
Whereas for the Medical field, you have to answer NEET UG examination. The state Counseling will depend on your NEET score, so will your 15% AIQ Counseling, if you have applied for it. So don't worry about answering any other Examination, unless you are answering for AIIMS and JIPMER as these are the only Examinations that are conducted apart from NEET .

For admission to any college the scores obtained in the National Eligibility cum Entrance Examination or NEET play the most important role. The scores obtained in the examination will determine the ranking in the All India charts of selected candidates. The rank in turn will determine which college a candidate can opt for from the vast list of medical colleges spread across the country. 
The COMEDK exam as such has been withdrawn and incorporated into the NEET UG exam. 
Also, the scores will be treated equally in both government and private medical colleges. There is no separate criteria of marks for getting admitted to government and private medical colleges across the country. 
For any further assistance feel free to refer back here. 
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Good Luck for your Preparations!