How can I repay the hospital, knowing that I conducted tests for my wife there without the administration's knowledge, and it was not an emergency, and attempting to pay now might cause problems for me and my colleagues?

Allah Almighty commanded the fulfillment of contracts. What you did by conducting examinations for your wife in the hospital is a breach of the contract and the condition. The expiation for this is that you repent to Allah and resolve not to return to such an act again, and that you pay the cost of these examinations to the hospital in a way that does not cause harm to you or your colleagues. You should also advise your colleagues to fear Allah and safeguard trusts by not conducting examinations except for those who are entitled to them.