Yes, you can request your original certificates back from the college if you decide to drop the course due to health reasons and wish to join a degree program in your hometown. Colleges are required to return original documents upon withdrawal of admission, though the process may vary depending on the institution's policies.

Here's what you should do:

1. **Submit a Formal Application**: Write a formal letter to the college administration explaining your situation, including your health condition, and request the return of your original certificates.

2. **Consult Admission Policies**: Review the college's admission and withdrawal policies. Some colleges may charge a nominal fee or deduct a portion of the fee for administrative purposes when withdrawing.

3. **Provide Medical Proof**: If your health condition is a significant reason for withdrawal, it might help to attach a medical certificate or proof to support your case, as this may expedite the process.

4. **Meet Deadlines**: Ensure that you follow any deadlines mentioned in the college's withdrawal policy to avoid complications in retrieving your documents.

By following these steps and clearly communicating with the college administration, you should be able to retrieve your original certificates and move forward with your plans to pursue a degree in your hometown.