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Try to avoid playing through pain as much as possible. Anti-inflammatories like ibuprofen or naproxen sodium (aleve) before and after practice - a doctor might recommend taking 3 doses of 3 ibuprofen daily (don't remember how much naproxen sodium that would be, but I've been prescribed both in the past).
Ice packs - immediately after playing, and a few times throughout the day, particularly if you feel it flaring up.
Wrist brace - definitely spend the money on wrist braces, they're cheap, you should be able to get both hands for $30 (Stay away from Futura or anything you can get at a big box store - order a set of these: [link]). If your hand/wrist feels weak or painful during daily activities, wear the brace (and stop doing the activities, if possible). Wear them at night - you might be a little sore in the morning at first afterwards, but just stretch a little and give them a bit of a massage to limber up again and it'll go away. Don't wear them during playing - you'll alter your technique and probably just end up hurting yourself with non-ergonomic playing that will stress your joints and weaker muscles.
Stretches - if they don't hurt. You can just look up basic wrist/forearm stretches and do them a few minutes before leaving for band practice.
Cortisone injection - if the pain gets really bad and isn't going away, your doctor may mention a cortisone injection. It'll be painful (I fainted after receiving one in my wrist) but it could help reduce the swelling. I'd save this for a last resort, though.
Rest - if it hurts, stop. Don't play through pain. I know you will, though, so try to at least take breaks at practice - a little extra time between songs, maybe a 15 minute break at the halfway point. If possible, see if you can move to biweekly practicing for a while. If you've had problems since January, you just keep re-injuring yourself, and once something like this turns chronic you really need to stop and have it evaluated by a professional.
I'd recommend going to a doctor, and possibly physical/occupational therapy if you can afford it and doc recommends it. Even if you can only afford one session, they will print up a bunch of exercises and stretches you can do to help prevent it in the future, and could possibly check out your technique and recommend alterations (rotating your wrist inwards so your hat technique looks more like a door knocking motion, or something like that).
Finally, there is the possibility that it is not tendonitis but tendinosis, which is more serious and long-term ([link] or [link]). In that case, your tendons are degenerating from micro-tears not healing properly due to repetitive motion without sufficient recovery time, causing scar tissue buildup inside your tendons, and you have to to treat it differently than you would an inflammation (basically, tear apart and rebuild the tendon over time through eccentric load exercises - not as bad as it sounds, it mostly just involves 20 minutes of resistance band exercise a day for a few months). I've had medical treatment for both issues in the past, and you can recover within 1-3 months if you follow your doctor's orders. Unfortunately, if they say stop playing, you need to stop playing. If you must play, ONLY play for shows and full band practice sessions.