Athough the animosity between Philip the Handsome and Ferdinand the Catholic was more than evident, there is no evidence of Philip having been poisoned. We have a very detailed account of the illness process suffered by Philip the Handsome, coming frome Doctor Parra, one of the physicians who assisted him, and he coments on the rumours of poisoning, but dismisses them. I'll quote his report on the symptomatology, as it will be helpful:

King Philip, may he be in glory, had very recently played ball in a cold place for two or three hours before he got sick, and he had let himself cool down without covering himself.

Thursay 16th of September the King woke up unwell, it is thought that with a fever that never left him till he died [...].

The following friday he still had a fever, but did not say anything, and ate nearly healthy, though without much appetite.

Saturday he continued the same until the evening, when he was so cold that he could not hide it, and then he called two physicians and told them what he felt, and what up to then he had not told, and that thursday and friday he had felt that same cold, but milder. This saturday, on that cold he had a strong fever.

Sunday he was with fever, and with pain on the side, and he spat blood. [...]

Monday morning, that was the fifth day, he woke up with a fever and with the uvula so swole, and also the tongue and the palate, that he could barely swallow saliva or speak. [...]

Tuesday, that is six days of his suffering, he had to be purged, and woke up to the chamber pot by himself, and he went to the chamber six or seven times. In the afternoon, his cold came back, and his fever was stronger, as the other days. [...]

This day wednesday, at the accustomed hour, and it was the seventh day, his cold came stronger than it used to, and after that came a sweat throughout the whole body, warm, and very copious, that they thought he would be cured or at least much better. He had sweated for six hours or close to that, when a weakness came to him, all of his senses disturbed, and the tongue, and the speech, and from then on hardly anything he said could be understood, and he was alienated and with subet, that is a sleepiness so strong that could hardly be woke up.

Thursday, he was the whole day in that disposition. I managed to see him that thursday at two past midnight, and found him so conquered by sickness and his strength so gone, that there was no hope or chance of remedy. [...]

These are the symptoms, day by day, as reported by Doctor Parra on October the 11th in a report to the King. I would very much invite a doctor to check these symptoms, but as far as I have consulted with some doctors, the symptoms match some sort of bacterial infection. Of course, rumours of poisoning are mentioned even in the final lines of the report, but Parra considers them baseless according to his expertise and that of the rest of the physicians that assisted Philip. I quote Parra again:

Later it has been said among the Flemish populace, and even the Castilian one, that he had been given herbs. I did not see in him signs of such thing, and neither his physicians had any such suspicion or thought when I was there. The truth is that the matter was much, and for his silence was it badly helped, and for being much it turned malicious.

Ferdinand did benefit from the demise of Philip the Handsome, as he later acted as Governor General of the Kingdoms of Castile and León for ten years, but nothing indicates that he had a hand in the death of King Philip. As for the death of Alfonso of Portugal, I don't know the details, and don't think there would be a report as detailed as this.

​

Source:

SALVÁ, Miguel and SAINZ DE BARANDA, Pedro (1846), Colección de Documentos inéditos para la Historia de España. Madrid: Viuda de Calero. Volume VIII, pages 393-7. Digitised here