Southwest does not have first class, although I believe the very first row has some extra legroom. Some seats in the exit rows have extra room as well, but you wouldn't be able to sit there due to your disability. Here is some information on how Southwest can accommodate you:
https://www.southwest.com/html/customer-service/unique-travel-needs/customers-with-disabilities-pol....
Advance notice of disability
Customers with disabilities are not required to provide advance notice of the need for assistance; however, doing so helps us better prepare for the number of Customers who will need our help.
We give Customers the opportunity to proactively notify Southwest Airlines of any specific disability-related needs during and after booking.
When booking a new reservation, Customers may use the “Special Assistance” link on the Passenger & Payment Info page to indicate that he/she requires assistance. When booking online, Customers may notice that there is a link (identified with an italicized "i") that directs the user to the details of our policies for assisting Passengers with disabilities. After the Customer has selected his/her option(s), the Customer should scroll down and complete the booking process.
If a reservation has already been created, simply click on the “FLIGHT | HOTEL | CAR | VACATIONS” link located on the top of our home page. Then, select “Manage Reservations” from the “Flight” column, input the required information, and select “Search.” From that page, click on the "Special Assistance" link under the Passenger name. Once a Customer has added his/her option(s), the Customer should click “Update Information” and the information will be saved to the Customer’s reservation.
Customers may also advise us of any disability-related travel needs at the time of booking by telephone or, if a reservation has already been made, by calling 1-800-I-FLY-SWA (1-800-435-9792) prior to travel.
We recommend that Customers arrive at the airport no later than the recommended airport arrival time. If traveling with a power wheelchair, in the event that we need to prepare the wheelchair for stowage, we may ask that Customers relinquish his/her power wheelchair up to an hour in advance of departure. In this case, the Customer will be transferred to an airport wheelchair until boarding begins.
If traveling in a group of 10 or more Customers who use wheelchairs, please advise us at least 24 hours in advance by calling 1-800-I-FLY-SWA (1-800-435-9792) so that we can ensure adequate staffing and room in the cargo compartment of the aircraft for the wheelchairs.
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--Jessica
