That's a very simplistic view of economics. The US is the world's largest market for just about everything. It creates enough wealth domestically that its citizens can afford to buy from other countries without bankrupting themselves or the nation. Read up on GDP, fractional banking, stock issuance, sovereign debt, oil as a commodity, and reserve currency.

Even if that's true, is a trade war (which seems to be hurting some of our exports anyway…) the way to fix the trade balance?

Tariff money is supposed to subsidize the industries harmed by the tariff. There is an inequality in goods in which the US has a major advantage. To put it simply, it's much easier for us to grow soy than it is for China to replicate our technology. Furthermore, the Chinese economy is not doing nearly as well as the US which means we are in a position of power at the moment. It is extremely important that the US minimizes its trade deficit even if it's a dose of medicine for the consumer that they don't initially like. They will like it when jobs move back to the US or even Mexico that were once overseas.

People wonder where all this wealth inequality is coming from when it's as plain as day. The inequality is coming from the fact that large companies are taking jobs that were performed domestically, and shipping them overseas where there are less regulations and cheaper labor. They then sell that same good at the same price to the domestic consumer who no longer has that job. Do that with enough industries and only the people who actually own the company stand to come out on top. That is why the middle class is shrinking.

> a dose of medicine for the consumer

seems like there's a risk of:

higher labor and materials costs leading to higher prices, leading to lower sales, leading to reduced revenue, leading to workforce reductions, leading to lower sales, leading to reduced revenue, leading to workforce reductions...

ie a basic recession spiral.

An efficient market prevents any sort of death spiral. The objective of a tariff, just like the objective of regulation, is to encourage/discourage a certain practice but that doesn't mean there aren't ways around them if they become overly burdensome. For example, when environmental regulations become too burdensome, outsource the job to a place where those regulations aren't present. This is why environmental laws can easily put American companies at an extreme disadvantage and should be carefully considered. A lot of the higher costs you are worried about are self-inflicted because of all the ridiculous overhead required to run a business now a days.