Let's leave out the "I'm afraid" part for a while. "too" means "excessively" so "I'm too busy (today)" would normally imply that "I don't have the time to do what you want me to do" (I'm too busy to help you). "I'm very busy (today)" ("very" = "really/to a considerable degree") in certain circumstances could imply that "I'm still going to help you even though I have a lot of other things to do", but on the other hand "I'm afraid" seems to introduce your refusal to help right at the beginning.
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