Dear Riya

Provided you apply for MBBS state quota counselling in both the states, you will be able to claim MBBS seats under 85% state quota in both Delhi and UP, since you fulfill Delhi's eligibility requirement which requires one to have passed Class 12 from the state, and also fulfill UP eligibility criteria which requires one to be either a domicile of the state or have passed Class 10 and 12 from the state. 

Coming to NEET application form and you  written UP there, I do not think it should have any impact on your eligibility for both UP and Delhi state counselling, since  the time of counselling of states, NEET admit card and rank letter are all you will need, not the application form. 

Hope it helps. 

You can know more about UP and Delhi MBBS counselling criteria from below articles. 

UP MBBS Admission 2018

Delhi MBBS Admission 2018

All the best!