If you’re allowed to eat cookies after dinner but your brother isn’t, don’t say it aloud. To be allowed to do something is to have permission, but to say something aloud is to speak it.
Allowed is the past tense of the verb allow, which means to let something happen. It usually comes from a person with authority, like a parent who says you’re allowed to stay up late or a dentist who says you’re not allowed to brush your teeth with chocolate. Here are some examples:
Older students are allowed to roam until the bell but ninth-graders are herded into the auditorium. (Speak)
As soon as the group gathered, the delegates began to debate whether women should be allowed to participate. (Votes for Women)
Aloud sounds a lot like "out loud," which means basically the same thing, even though the word aloud is older and more formal. Aloud originally meant "to be loud," but now it means speaking something instead of just thinking it. Feel free to read these examples aloud:
She read Wilbur’s lines and heard Kelly echo back the words she had read aloud moments ago. (George)
I found myself singing aloud this song that filled my head like the buzz of a trapped fly. (Ophelia)
If you’re allowed to say these words aloud, you’ll notice they sound the same. You’ll need to write them to see that allowed has a w, while aloud is more like loud.