Your Donegal friend is right, RonnieBirtles. It is either Ush-een or Osh-een, depending on regional accent. It couldn't be Oh-sheen unless the O had a fada, which it doesn't normally though the two you know might have tacked fadas on.
Nothing wrong with Mairéad -- it normally has a fada on the E but sometimes people use a fada on the first A also, making the pronunciation Maw-raid instead of Mah-RAID.
An Irish 'Caitríona' would need to have the two Is there on either side of the consonants. If a slender vowel precedes a consonant then then the consonant must be followed by a slender vowel (I and E are slender).
Spelling reform in Irish was undertaken very successfully during the last century. The letter H was added in place of the dot over a consonant to indicate lenition (softening) of the consonant where grammar dictated a change in spelling and pronunciation. Many superfluous letters were cast aside in favour of more streamlined spellings although with the sound preserved -- I think this task is far easier when a language is only spoken by a minority and basically mostly taught in schools as opposed to one used daily by millions.
One example of spelling reform is the name Mairéad, which was reduced from Mairghréad via Maighréad to its current form. The old spelling Maighréad is recalled in the Máiréad form, as it would have been pronounced Maw-raid in some accents. Another example of spelling reform in action is the slimming down of Orfhlaith via Orlaith to Orla. The old spelling indicates the meaning better (flaith = princess) but the pronunciation is the same no matter how you spell it.