As a CS major too, I’m sure there are free spaces even if you are a CS major.
If logical reasoning (proofs) comes more naturally for you, I don’t think it is impossible.
Otherwise, Apostol’s book would have killed me with CS. I had lots of spare time and uhmm…I don’t think I attend a horrible school. It is ranked within the top 5 nationally in USNews ranking…
I been regularly taking 18 credits and it doesn’t seem to be a problem for me even when my other classes (notably math) are advanced classes… (and I had 2 part time jobs and friends)
That said, if you are a CS major, gl if you are planning to party all your 4 years.
I think that part will be a huge stretch unless you only do the bare minimums…