Yes , I have seen and fixed this exact problem you have described several times by replacing both those parts, i cant think of a instance where it has not completely fixed the problem. Make sure you follow the guide correctly. keep track of which skews go where, you only need to watch the iPhone 6 Logic Board Antenna Flex Cable guide to fix both. take your time.
1. Is the coloured frame of your 5c in good condition? the touch can sometime play up if there is to much pressure on parts of the screen due to damage to the coloured frame. (you can buy new frames if yours is damaged) 2. Is the software up to date? Is the phones storage full? make sure its updated and free up some space if you have less then 1GB free, then try backing up then factory resetting the phone. 3. If there is still a problem i would say you have bad quality screens and a new original or good quality replacement should fix the problem.