I'm not a native Portuguese speaker, and what I'm about to explain may not be accurate since I "learned" it from deduction based on my personal exposure to Portuguese. That being said...
The suffixes "-inho" (masc), "-inha" (fem.) indicate diminutive. The diminutive indicates that the given thing is "little". For instance "garoto" means "boy" where as "garotinho" means "little boy".
However the diminutive is usually used to sound more kind, sweet, or friendly. Just like in English "little boy" (or buddy), sounds friendlier than "boy". But in Portuguese it's not only applied to people but also to objects or adjectives. For example "cafezinho" (instead of "café"), or sozinho (instead of "só").
As you may have noticed if the original word doesn't end in a consonant then before appending the -inho/-inha suffix either the trailing vowel is dropped or a "z" is used to connect them.
Brazilians are very kind and friendly people, so expect to hear diminutives a lot.
Etymology: From só + -z- + -inho
Note for Duolingo: Guys, you should add a diminutive lesson.
It is a reflexive pronoun. Sentir used alone always require the direct object to be a noun. e.g.: Eu estou sentindo tristeza (I'm feeling sadness) so you are always feeling something else.
When you use a reflexive pronoun, you become the object for the action (sentir) and what comes next is a Mode adverb for how you feel yourself
So Eu estou me sentindo triste means I'm feeling sad.
I hope to have been clear enough. Although I'm native brazilian, we do not receive enough education on this sort of grammar so I may have made some mistake here and stand to be corrected.