Please find below the list of things I recommend to bring from Pakistan to America. You can modify the list as you see best:
Lota (I have a watering can I bought from here)
Traditional Dress
Formal Suits: If you don't have one, can easily buy from here
Jackets and long boots: It gets cold! You can easily buy from here
Shan/National Masala
Knorr Chicken Cubes
Knorr Soups
Dollars: 10,000 is the legal limit I think
Bedsheets: or you can buy from here
Towels: or you can buy from here
Passport/I 20
Lipton Tea bags: PK tea is hard to find in some places
Johar Joshanda: I am perpetually flu-ey
Medicines (Augementin, panadol cf etc): Medicines here are expensive and hard to get. Meaning for anti biotics, you need to be prescribed and doctor visits are costly. If you have a particular love for paracetamol/panadol woh bhi le kar aana because you only get ibuprofen and acetaminophen over the counter
Face creams: you get all the cosmetics here except that the face creams are often tanning. Now if you don't like that, I suggest bring 1-2 moisturizers with you (esp if you like creams with whitening ingredients)
Clothes
International License
Converter: For appliances that have non US chargers
Unilever products like Close Up, shampoos: P and G is more widely available here.
Extra eye glasses/lenses: Eye and dental insurance is often not included in regular health care plans
Jaaye namaaz/ tasbeeh/ head scarves etc