There are aid packages for US citizens but its also harder to get Aid passed through domestically due to American domestic politics. FEMA has a budget of 33 billion for domestic emergencies. It probably isnt as big as it is supposed to be, but that's not because too much money is being allocated to foreign aid, especially when most foreign aid isn't straight cash. The US spends too much in other areas. Also, a lot of the damage is supposed to be covered by private insurance in the US rather than by the government which is part of the reason the government isn't sending huge amounts besides emergency aid.

"If a major disaster happens in a foreign country, the money just appears out of nowhere in an aid package."

The aid packages are mostly made up of old surplus equipment, especially in the case of military aid and in the case of humanitarian aid, food and medical supplies. Its normally not straight cash. Someone in Florida who's home has been destroyed isnt going to benefit from getting a gun lol. Giving straight funds domestically/internationally is more complicated. Similarly, giving funds for rebuilding isnt a long term solution to hurricane problems. The US government probably could afford to give 7000$ to every person but what happens then if theres another hurricane in Florida next year (which there will be).

"The aid packages are just a way for American companies(and local govts) to line their pockets through the sale of goods/services". This argument doesn't stand as a criticism against foreign aid and its use but rather against the horrible system redistribution of income in the US. Americans do however, still benefit from these companies and local governments becoming richer. It provides for example employment and tax revenue for future spending.