How can one avoid carry bags when queuing for the security checkpoint in an airport?

A medical certificate is unlikely to be of that much help. It's possible that presenting one would allow you to keep a trolley in the queue, but there's really not any kind of standardized procedure for that, so it simply comes down to whatever employee happens to be overseeing the checkpoint, and that person is likely to be busy, not really interested in your individual situation, and may not even speak your language. Even if you can keep a trolley with you in the queue, the airport isn't going to allow you to bring it through security, so you'll have the same problem carrying your bags to your gate and throughout the rest of your journey.

But there are alternatives:

• Pack light. Check everything except the essentials that must be hand-carried.
• Bring your own wheels. Use a carry-on bag with built-in wheels. Beyond the usual full-size carry-on bags, they also make smaller laptop bags and even backpacks with wheels, which are small enough to fit under the seat in front of you if necessary, so you can keep them even if there's no overhead bin space left. Or fit your own bag to a folding luggage cart.
• Request assistance. Airports and airlines have arrangements for people with disabilities to provide required assistance. This assistance often involves wheelchair or golf cart service, but can take different forms depending on your individual needs. Someone will escort you through security and will bring your bag along if you cannot carry it yourself. The process to receive this kind of assistance varies depending on the airport, but it can usually be requested through your airline. Airline and airport websites usually have further information on their services on their accessibility pages.