Very cool! Yes it sounds like there is a problem. Check the position of your mouthpiece on the neck, it should be about half way on the cork.
It could be that you are playing very very flat, but it could be your sax has a major problem so I can’t tell you from here!
There is a way to tell if your sax is in tune with itself….
Play a low Bb, then overblow to hit an F, but without changing the fingering. So, you are fingering low Bb but playing a low F. If you can do this and hear the F sound in tune to the regular fingered F then your horn is playing in tune.
Hope this makes sense!
Johnny
