I would like to know if I take doxycycline at 7 pm is it safe to take melatonin at 9pm?

The meds you are on do not interact, so you are fine.

"Interactions between your drugs
No drug ⬌ drug interactions were found between the drugs in your list. However, this does not necessarily mean no drug interactions exist. Always consult your health care provider."

There are 3 drug and food interactions, 2 moderate and 1 minor meaning;

Moderate Moderately clinically significant. Usually avoid combinations; use it only under special circumstances.

Minor Minimally clinically significant. Minimize risk; assess risk and consider an alternative drug, take steps to circumvent the interaction risk and/or institute a monitoring plan.

Click on the link provided by Drugs.com in order to access the full interaction report:
https://www.drugs.com/interactions-check.php?drug_list=940-0,1548-0

If you have any concerns always contact your DR..

Regards, masso