Dairy sensitivity - reintroducing

I gave up dairy almost a year ago when my son was a month old and he was diagnosed with a sensitivity. Now that he’s over a year, his doctor said I can try putting it back in my diet, and if that goes well to start him on yogurt.

Anyone else go through this process? I tried small amounts twice so far (today is the second time). Each time I’ve been sick to my stomach afterward. I would really like cheese back in my life so I will try more. But for anyone who’s gone through the process: how long did it take, any suggestions?