I'm assuming after 10mins then you are getting a pleasant vape, you describe harsh, are you getting a burnt taste? Are you priming the coil when using for the first time, dropping liquid into the wicking holes then let it sit in the juice,
Also when new coil in start it off at low wattage, take a few pulls then increase slightly each time till you get to desired wattage, this will help with the life of the coil
If you are getting a burnt taste you have probably burnt the cotton and best thing to do is empty the juice give it a good clean in hot water then insert new coil and take steps as above,
28w is the highest of the recommended range as they are rated between 20-28w
Additionally like @matty2k said above, if you're not after the throat hit, and are after a nicotine fix give some 10 or 20mg nic salts a go, 10ml bottle and see how you get on with them
They are normally 50/50 liquid