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.
In regard to the ruling of migration from a non-Muslim country to a Muslim country, we have already discussed this in Fatwa 86405. We clarified in this Fatwa that migration may be an obligation and it may be desirable. Even if we presume that migration is not an obligation on you, in our view, it is better for you to migrate to reside in a Muslim country if you can do so, especially that you are a new Muslim as you mentioned, and you need what would help you to be steadfast on your religion. You undoubtedly know that there are many causes of affliction like misconceptions and desires in non-Muslim countries, and no doubt the benefit of protecting your religion should take priority over anything else.
As regards your mother, you are obliged to be kind and dutiful to her. Indeed, you may achieve this even when you reside far from her, like by phoning her to ask about her, helping her financially, sending some gifts to her and visiting her sometimes.
Moreover, the best means of being kind and dutiful to your mother is to call her to Islam and clarify to her its good traits especially by your conduct with her. In doing so, you may make use of the following Fataawa: 111063, 81979, 88906, 88051, and 85234.
Allaah Knows best.