Car feels wobbly/unstable at higher speeds?

I have a 2007 Mazda 3, and recently has
been feeling off. Today especially, it just felt
really wobbly and unstable at higher speeds
(anywhere from 60+ mph)
I had to replace the rear driver side tire due
to a nasty gash in the original, the tire is
used and obviously not the same as the
other 3 but never felt it caused any
problems. My dad said it is a little off, not
exactly sure if he said it was wobbly or
loose or what, but didn't seem like it's cause
for extreme concern. Again, never seemed
to have any issues when I first replaced it.
My dad drove it a couple days ago and I
asked him if he noticed anything off, he
mentioned that the suspension is a little
wobbly.
Today the steering seemed off as well, not
sure how to describe it, but felt a little stiffer
than I'm used to.
Checked all the tires, they all seem pretty
solid (no flats, nothing loose)
Generally, just felt very uncomfortable
driving. Was very nervous the entire way
home.
And finally, I believe it might just be the
nervousness everything else was causing
me, but my acceleration seemed to lack a
little too. I'm pretty sure that's just me being
paranoid.
I honestly don't know what to do or what
could be going on. Should I just go ahead
and get everything looked at?