In your example, noises started at a certain point in the past and ended at a certain later point in the past, so in this case you can use the past perfect continuous tense (Englishpage.com):
I had been hearing some strange noises for the past two days after
waking up and it had been scaring me, so I'm glad it did not
(It did not happen today is in the past tense, because it refers to a distinct time in the past.)
If the noises started 2 days ago and they still last, you say it in the present perfect continuous tense (Englishpage.com):
I have been hearing...
You can also use the past simple tense for something that started and ended in the past (Englishpage.com):
I heard some strange noises for two days.
In this case, the emphasis is on when you heard noises and not for how long they were lasting.
The past continuous tense is usually reserved for ongoing actions in the past that were interrupted by another (usually short) event in the past (Englishpage.com), so it may not be best for your example.
So, you can write all parts of the sentence in the past tense:
I heard some strange noises for the past two days after waking up and
it scared me a lot; I'm glad it did not happen today.
You have two sentences, so you need to separate them with a semicolon or just write it as two sentences.