It happens, I call it gi burn. (As opposed to mat burn)
I have soooo been there.
Whoever it was seems to be applying alot of leverage on the collar grip,causing friction between the collar and your neck. Pharmacies can give you a lotion that will reduce the pain. When you wake up do some neck stretches to loosen it up a bit. Roll your head up,down and around. It shouldn't happen often,if it does then your partner should be made aware that it's harming you. Sometimes in randori things get a little rough,but it shouldn't be a regular occurrence. It was your first session so expect one or two bruises/aches. Keep it up.
Train hard,fight harder,live better.
Ice it for no more than 10 minutes twice a day for a few days and don't aggravate it with massaging if it made it worse. If you feel any numbness or tingling in your fingers or toes then go to a doctor for an x ray. When it gets better, ask you coach/sensei for exercises for your neck to keep that from happening.
I suggest that judo may not be the martial art for you. Go for a more leaner martial art, like Tai Chi.
Yesterday my friend took me to a Judo session and today my neck has been killing me and is achey I know my body's not used to it and I was warned but my mum gave me a neck massage and it got worse any suggestions