If I catch toxoplasmosis, am I infected for life?

No. In people with a normal immune system, toxoplasmisis is a self-limited disease. In people who are immunocompromized, such as HIV or organ transplant patients, the disease can reactivate.
If you are a healthy. 23 yr old, then no. If you have HIV or other issues, you may have longer term issues. One other issue, is that if you do develop toxoplasmosis. You can have asymptomatic, permanent nodules present for years that are not active disease but more like scar tissue. Nothing to worry about, but make sure to keep in your medical history in the future.