My son had similar problems. He had constant ear infections starting when he was 16 months old, and it did affect his speech. Although he did speak a few words at age 2, they were all partial words - like "ba" for "banana", "ga" for "grandma", or "ma" for "mommy".
We expected immediate improvement after the ear tubes were inserted (age 2), but it didn't happen. It was gradual improvement with weekly speech therapy.
The tubes fell out after a few months, and he was still experiencing ear infections, so they had to insert larger ones (age 3) and they removed his adenoids (which were enlarged). These tubes fell out, too, but he no longer has problems with ear infections.
Now, at age 5, his speech is normal. He hasn't had speech therapy in over a year.
BTW, I'd never heard of dairy causing ear infections. My son has always loved his milk. But, if that was the cause, he must have grown out of it. He still drinks lots of milk, and he doesn't get ear infections any more.
You may already know this, but your son may qualify for state help with Early Intervention/Help Me Grow. Your pediatrician can give you the contact information. They helped my son quite a bit.