Allegiance and loyalty are synonyms. Both are nouns. They are defined in terms of each other:

loyalty
Word forms: plural loyalties
uncountable noun
Loyalty is the quality of staying firm in your friendship or support for someone or something.
I have sworn an oath of loyalty to the monarchy. [+ to]
This is seen as a reward for the army's loyalty during a barracks revolt earlier this month.
Synonyms: faithfulness, commitment, devotion, allegiance

allegiance
Word forms: plural allegiances
variable noun
Your allegiance is your support for and loyalty to a particular group, person, or belief.
My allegiance to Kendall and his company ran deep. [+ to]
...a community driven by strong ties and allegiances.
Synonyms: loyalty, duty, obligation, devotion

--Collins COBUILD Advanced Learner’s Dictionary. Copyright © HarperCollins Publishers