I was just prescribed zithromax 1gram and i ate a little bit of some shredded cheese right before i took my dose, will the medicine absorb properly?

It should be ok: Azithromycin's absorption is not altered by food.

Yes: Nothing to worry about. It is beneficial to eat something while you are taking antibiotics. You will have less stomach trouble if you take them with a meal! Hope this helps!

Small amount: Unlikely to interfere with absorption. It should be fine. All the best.

No worries: Its OK to have dairy food while on Zithromax. Not contraindicated.