All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and Messenger.
Combining Thuhr and ‘Asr prayers because of rain is a controversial issue among the jurists . The view we adopt here in Islamweb is that this is permissible but it is not permissible for a person who prays individually to combine two prayers because of rain, because the Sharee’ah permitted combining two prayers due to rain for the difficulty of going to the mosque twice in a rainy weather, and out of urging to observe the prayers in congregation. However, this reason which permits combining the prayers is not available in regard to an individual person because he is not praying in congregation, and there is no difficulty for him since he will pray individually. Therefore, you were wrong in combining the prayer individually (on your own) and you are obliged to make it up.
For more benefit, please refer to Fatwa 88927.
Allaah Knows best.