Modal verbs are tricky: each has only two forms (must has only one) to express a very large range of times and "realities", and each has multiple senses: deontic (obligation), epistemic (inference/probability), and dynamic (capability/intention). And their use in conditional constructions is even more complicated, because conditionals many different sorts of logical and temporal and even social relationships between the condition (if) clause and the consequence (then) clause.
But in this particular case there is no ambiguity; this sentence is not possible:
∗ If I had won the competition I will be going to Florida next week.
The construction will be going entails a factual consequence—an assertion that it the event is a necessary consequence if the condition is met. A factual consequence must be possible: it demands either an open condition—one held to be possible—or a certain condition—one known to be a fact:
OPEN: If I win the competition this afternoon I will be going to Florida next week.
CERTAIN: If, as you tell me, I have won the competition, I will be going to Florida next week.
But in this context, the past-perfect construction in the condition clause can only be understood as a counterfactual—it is known that you did not in fact win. (It is not a ‘true’ perfect construction but the perfect employed to mark past time-reference where the past form signifies non-factuality.) Such a counterfactual condition requires a nonfactual consequence:
If I had won the competition I would be going to Florida next week.
∗ marks an utterance as ungrammatical