I've had this problem with the thumb and fingers before. I train 4~6 hours daily which include a lot of cardio-based exercises for boxing so my joints do take a beating sometimes. I've taken GenoFlex and Cissus XT, while they did provide pain relief for my shins (caused by running/jump rope/agility ladder etc), they didn't do anything for my fingers/thumbs.
Last year, I seriously busted my right thumb in a match, I couldn't grab anything with my right hand for about 2 weeks. Luckily I'm a Southpaw, so doing everyday things was okay. I took Cissus XT, iForce Joint Help at that time and it didn't do anything for it. However, E-Pharm's Joint Force did provide temporarily relief. I would spray it, and massage onto it into my hands and forearms before putting on my handwraps and gloves. I visited several masseurs, and they showed me how to massage it. It was ****ing painful, but afterwards you'll feel better. They will apply pressure and massage on your fingers/thumb, do some movements with that particular thumb/finger to prevent scar tissue from building up, and massage the tendons along your forearm, because there is one huge tendon that stretches from the elbow to your thumb. I memorized what they did and massaged it almost everyday, and you have to be patient with it. It took me almost half a year for the pain to disappear 90%. I adjusted my hook punch to ensure that it'll never happen again.
IMO, I don't think a supplement will fix the issue... You just need to properly warm up and focus on technique for now, and perhaps see a physical therapist/or a good masseur.
Edit:
Right now, I have a minor discomfort (but not serious) with my left index finger and left thumb since the start of February this year. I took GenoFlex on March, and it didn't do anything for my left finger/left thumb. It did provide relief for my shins and continued to work after I stopped taking it. I always make sure to put extra effort in warming up my left arm and hand. Oh yeah, the problem could also be the quality of your gloves. If you don't have good quality gloves, you may to invest in a good quality pair (I don't have much expertise in MMA gloves so don't ask me for recommendations). I've seen some people who have ****ed up their hands because they didn't wrap their gloves properly or they wore ****ty cheap gloves.