Replacement tub bearings are available. You'll also need a stem seal kit and a spanner wrench for the tub nut.
Its a big job but doable for a DIY'er but I would eliminate other possibilities first. Hopefully the agitator shaft isn't rusted or pitted, thats important for a good seal with the new stem mount.
I will check other things as you suggested, there is no set screw on my agitator how do you remove that from the shaft? What other problems should I look for first .
Thank you