Topical finasteride has the same active ingredient as oral finasteride, which can sometimes cause sexual dysfunction and symptoms of depression. You may also experience mild side effects on your scalp—including irritation, itching, a burning sensation, and dryness—especially in the first few weeks of using the medication. Typically, these go away with time.
It's possible, but rarer, to experience side effects from topical minoxidil, which may include itching and irritation at the application site, signs of an allergic reaction (e.g., rash, hives, or difficulty breathing), facial or body hair growth in areas other than the application site, and changes in hair color or texture.
Finally, you may experience shedding during the first few weeks. This is normal and, while it might cause some worry at first, it shouldn't be a reason for you to panic or stop taking this medication. Extra shedding will resolve as the new hair grows in (usually in about a month).