It’s not at all uncommon to have a reaction with the first rituxan infusion. I did too. It’s quickly halted with Benadryl and then generally the subsequent infusions are well tolerated.
If his oncologist said your husband can just be monitored then that’s good. Just as long as he keeps following through with appointments. This can be slow to develop but you don’t want to let it get out of control.

Just to refresh, if you look back at my Aug 9 reply you’ll see the explanation for why your husband was giving Rituximab and why it’s important to inhibit his B-cells even during a pandemic. Most of the time when an oncologist discusses meds, they won’t often go into the details of what happens and why it’s needed. I had substantial damage to my spine from a reaction with my bone marrow transplant. My B-cells attacked my spinal cord causing demyelination of the cord. Besides heavy steroids I was also given infusions of Rituximab at Mayo. At that time my transplant doctor and neurologist both explained in great detail why it was necessary to control the B-cells.

Yes they are extremely vital in our body’s immune defense but they can get out of control with a miscue, and attack our body instead of helping in an autoimmune attack. Your husband’s cancer from your initial explanation, is one caused by the overproduction of B-cells and they need to be held back. That takes precedence over a weakened immune system. And as I mentioned before, he already will have a weakened immune system from having a blood cancer and should be cautious with his cardiac amyloidosis and AFIB to avoid getting ill.
https://connect.mayoclinic.org/comment/624876/
I agree, sometime less is best! I hate taking meds but I’m living proof of better living through chemistry. ☺️

Wish your husband all the best from me on his labs next week. I’d like to keep up with how your husband is feeling. Will you let me know what he finds out?