OK, you aren't going to give yourself arthritis. Doesn't work that way. Tendinitis, maybe.

Possibilities:

1) The actual bone/cartilage structures are limiting ROM (Range Of Motion). If that's the case, nothing I can suggest will help.

2) The joint capsule is restricting ROM. The joint capsule is a sort of envelope around the joint that contains lubricating fluids and keeps crud out. It could be tight. In this case, it would be tight on the palm side. Sometimes it is tight because a fold has become stuck together - that's one possibility in frozen shoulder. If it is a fold, you are in big luck, because once you get it unstuck you've got it. Whether it is a fold or just tight, the tissue responds very slowly to gentle pressure. On the palm side, press against the joint until you feel you have kind of a grip on the tissue, and slide it to the side. Hold for between 90 seconds and 5 minutes, slide back to neutral position (this is important, just letting go isn't good) and let up, rub for circulation, and then repeat, sliding the other way. Also slide toward the finger and away from it. Don't press hard, don't slide hard. The tissue is kind of like Saran-wrap, it stretches if you apply gentle force for a long time. If the finger or thumb doing the work is getting tired, you are doing it too hard. If the hand you are working on hurts, you are doing it too hard. After a few repetitions, you should see a little increased ROM. If not, this isn't the restriction.

3) Ligaments are tight. The ligaments in question here are (probably - hands are ridiculously complicated and there are other structures that can restrict ROM) the ones running from the base of the finger to the heel of the hand. When you try to hyperextend (bend back) the finger you should be able to feel, and maybe see, the structure. Rub it, in a circular motion, along its whole length. Every once in a while, gently push the finger towards hyperextension. Ligaments are tough and take a ridiculous amount of work to relax. But it is possible.

For both of these, I can't stress enough: GENTLE. Slow and gentle. This is not a "no pain no gain" thing. If you push hard enough to hurt, you can cause damage, and the tissues will fight back and you will lose ROM instead of gaining. These are multi-session, multi-day processes. But if you are slow and gentle about it, even if you don't get the ROM you are looking for, you will do your hand good.