Is it permissible to omit wiping the inner ear during ablution if there is an inflammation that would be harmed by wiping it, knowing that it is not possible to place a cloth over it for wiping or to perform tayammum on this limb?

Wiping the ears during ablution is sunnah (recommended) and not obligatory according to the majority of scholars. There is no harm in not wiping the inner part of the ears, especially for those who are inconvenienced by it. Its ruling is similar to that of someone who omits a sunnah due to an excuse. Tayammum is not obligatory for omitting the recommended acts of ablution.