Of course your inspector should have seen any deficient conditions when you acquire the house. What was on the report?
On a two story the loads are quite large and you need to be proactive. Its not an ASAP situation but the longer you wait, the more distorted wood structure and flooring will get, and bent wood may not ever come back to its original shape.
There are decent honest P&B foundation folks out there. I would get several proposals and compare. There are also artists out there who will sell a widow on $12,000 worth of "repairs" that don't need to be done. Unless extra beams are added or replaced, and the crawl space is reasonably accessible, adding or adjusting a couple of interior piers should not cost more than $2000. It depends on your specific situation though.
John Pfister (281-480-6684) has been around a long time and does good work. He doesn't do huge house lifts but this sounds like his kind of job.
Murley is a larger outfit that does work in the Heights +. 281-447-3507.
Some sheetrock may need to be patched but that is cosmetic. If you have a structural issue under the house, that is more important.
Right now it hasn't rained in a while and most crawl spaces in town are nice and dry. Perfect time to do foundation work. After a couple of weeks of rain there will be a lot of ponding down below and jobs will have to be put off, as jacks will just bury themselves in the muck.