The correct option is
B I shall go either today or tomorrow.
A simple sentence has only one subject and predicate. It has a finite verb with a completed thought. A compound sentence has at least two parts (also referred to as a clause). Each part has its own subject and predicate and makes good sense by itself. Hence each clause is independent of the other and called the main clause or independent clause. The main clauses are connected using a co-ordinating conjunction (for, and, nor, but, or, yet, so).
A complex sentence has at least one main clause (which is an independent clause) and one or more dependent clauses, connected using a subordinate conjunction. The dependent clause cannot stand by itself and make good sense. It depends upon the main clause.
Option A: The two clauses viz (i) I shall go today and (ii) I shall go tomorrow, can stand independently and make good sense. They are independent clausesconnected using the co-ordinating conjunction-"or". Hence, this is a compound sentence and this answer is correct.
Option B: "So that" is a subordinating conjunction used to indicate cause-and-effect relationships. Here, one sentence is not the cause of the other. Hence, this conjunction cannot be used. This option is incorrect.
Option C: "Because" is a subordinating conjunction used to indicate cause/ reason. It connects an independent and dependent clause and forms a complex sentence. Here, one sentence is not the cause of the other. Hence, this conjunction cannot be used. This option is incorrect.
Option D: "If" is a subordinating conjunction which expresses a condition. It precedes a clause/ event which must happen first in order for the other event to occur. The clause, "I shall not go tomorrow" is an independent clause. The clause, "if I go today" cannot stand by itself and make good sense. It is dependent upon the above independent clause. Hence, this is a complex sentence and this option is incorrect.