a year in Ireland

This year has been a challenge to me . Even while homesick, I have not regretted going abroad at any time ; a year as an Erasmus  student allows one to test oneself in a new environment so as to show open-mindedness, determination, adaptation and self-reliance. NUIG has been an excellent host university, with a model organisation and a very lively student life. This is an experience from which one will grow richer personally speaking, and more self-confident.

This is fine,Crystal but I would write it as "I" and not as "one" which sounds rather formal and old fashioned to me.For example "This is an experience from which I will grow richer and more self confident" and omit "personally speaking".It's not really a grammar mistake but more a question of style.

A Year in Ireland

This year has thrown up (been) a new challenge for me. (to myself.) Even though (while) homesick, I have not for one minute / at any time .... regretted going abroad. (at any time;) A year as an Erasmus student provided the (perfect?) opportunity (allows one) to hone my personal skills,  (test oneself) in terms of being open-minded,determined, adaptive and self-reliant, in a new environment.  (, so as to show open-mindedness, determination, adaptation and self-reliance.) NUIG has been an excellent host university, with a model organisation and a very lively student life. This is an experience (from) which has not only enriched me academically but also improved my self-confidence. (has one will grow richer personally speaking, and more self-confident.)

Well written,Crystal. With reference to the title, most words should be in initial capitals to give it more credence. Your grammar is perfect but I have suggested a few more native phrases you may use to enhance your article. Your second sentence, with the semi-colon, seemed overly long so it would read better to maybe split the sentence in two (as suggested).