So, I want to have fog in URP. The problem is that the fog dosen’t apply when I look upwards. And it also does not apply to the upper part of high objects. Can I fix this without using any assets from the Store?
Seems you want to have a volumetric height fog, which is only in HDRP. You have to implement it yourself in URP or buy an asset, sorry. 
You can try my asset, which has height fog: https://assetstore.unity.com/packages/slug/215599