Whichever preposition is used here mean completely different things,
I travelled at the Philippines
Makes little sense and would not seem natural,
I travelled in the Philippines
Implies that you went to the Philippines that travelled around a bit.
The other alternative is talking about travelling to the Philippines which has a different denotation but may be what you're looking for:
I travelled to the Philippines
Implies that you went on a trip and the final destination was the Philippines.
In the end you have to choose what you mean by the sentence because each preposition changes its meaning.