Getting the battery tested is a good idea, sometimes in larger cities shops will make you wait around for a while to do the free service, and on weekends you can forget it. but if you have a good shop you know and they can do it for you quickly than by all means go for it. but for a two second quick look you should be able to use a multimeter to see what the voltage of the battery is with the car off. if its less than a 9 volt battery than the decision to go get the battery tested and probably replaced is a good call. If its up right at 12... And with the multimeter you should be able to check the battery with the car running to see if the charging system is doing its job. If the charging system isn't working than you can focus on that. Its tough because we can't see the car but... you have written that the car always starts. That doesn't sound like the bad batteries I've had: a really bad battery is going to have left you stranded, most likely after sitting all night following only a brief around the block ride.
you should have a multimeter anyway because... you'll want to know- if it is your battery that has gone bad- what if anything other than simply time and weather caused it, and for that you will need a multimeter.
1985 190e 2.3