Amino acid compatibility
It seems like you may be thinking along the lines of DNA, where adenine pairs only with thymine and guanine with cytosine.

Unlike DNA, amino acid chains are single-stranded...

...so there is no pairing of compatible types like there is in DNA. Neighboring amino acids in the chain can be in any combination (as you say, because each has a carboxyl group and an amino acid group), just as neighboring nucleotides in DNA (ie those next to, not across from, each other) can come in any order.

In practical terms, the functional groups of amino acids have different chemical properties (hydrophobic, hydrophilic, aromatic), therefore some pairings are probably more commonly found than others. But in principle there is no restriction on who is next to who.