Surge vs. surjo?
In the statement: Me surge una duda. Why is surge being used instead of surjo?
2 Answers
Because the subject of the verb is "una duda" or "it" if you need a subject pronoun.
A doubt arises to me.
It is another of Spanish's very common intransitive sentence constructions. Similar to the gustar-like verbs (me encanta..., etc.) They are confusing to English speakers as we usually phrase the same thought with a transitive verb and "I" would be the subject rather than "to me", an indirect object.
me gusta (it is pleasing to me)=I like in English.
When I see/hear/read X, it raises a/the doubt in my mind that (it causes me to wonder/think/ask myself). ...
There are many ways to express such ideas in English (and in Spanish). If you insist that the first way that pops into your head must have an exact equivalent in Spanish (and especially that the subject in English be the subject in Spanish) you are in for trouble. You must either learn to accept that there are different ways to say something (whether in a given language or, more especially, in another language) or give up any hope of learning another language.
Above all else, the idea that "my way" (the way of my language) is the the only way, is the single greatest obstacle to learning a second/third language.