The only non-stops on JFK-MAN and MAN-HAJ are Thomas Cook Airlines and Flybe, respectively.
I'm pretty sure this means you have bough the two tickets separately.
Of course, we'll consider you have taken into account the fact that the JFK-MAN flight is overnight, so if you leave from JFK on the 23rd, you'll be in MAN on the 24th, and your second flight should leave on that date.
On Thomas Cook Airlines, your hold luggage allowance depends on the fare:
- If you booked an "economy light" fare, no hold luggage is included.
- Otherwise, flights from the USA include one hold bag weighing 23 kg (50 pounds) max per passenger.
On Flybe, likewise, there are fares with or without hold luggage:
- A "Just fly" fare will not include any hold luggage
- Other fares will include one hold bag weighing 23 kg (50 pounds) max per passenger.
In both cases, if you bought a ticket without hold luggage included, you will have to pay extra to add luggage to your booking. It is usually cheaper to do it online in advance rather than at the airport.
As your two tickets are separate, this is what you will have to do in Manchester:
- go through immigration (passport control)
- reclaim your bags
- go through customs
- go to the departures area
- find the check-in desk for your second flight
- Check-in before the deadline for that flight.
- Go through security
- Go to your gate
- Board before the boarding deadline
It is quite possible that the check-in desk for the second flight will actually not be open. In most cases you can only drop your bags 2 hours before the flight at the earliest, so you'll be stuck with your luggage for about 5 hours.
If you need a wheelchair, you should contact each of the airlines, they will arrange that for you.