About the qada' (qaza) this is clear according to the Verse 185 in surat al-Baqara
[2:185] Ramadan is the month in which the Qur'an was sent down : this
Book is a perfect guidance for mankind and consists of clear teachings
which show the right way and are a criterion of Truth and falsehood.
Therefore from now on whoever witnesses it, it is obligatory on hire
to fast the whole month,
but if one be ill or on a journey, he should make up for the same number by fasting on other days.
Allah desires to show leniency to you and does not desire to show any
hardship. "therefore this method is being shown to you so that you may
complete the number of Fast days and glorify Allah for the Guidance He
has shown to you and be grateful to Him
And it is/was your right to break fast as you had a permission from Allah. Some madhabs may say one should try to fast or it's better to fast and others will even say you should take the opportunity of having a permission from Allah!
The only sin i can see is that if i got you right, you lied to your relatives from a fiqh point of view this won't break your fast it is still safe, but you have loosen tawab and ajr (rewards). To me it's not clear why you lied? because you had a permission not to fast!
I hope i could help!