What king of exercises should I start with?Open or close chain exercises?Or should I start with swimming?
Yikes. To be honest, you really really need to get an answer to this from a PT or from an orthopod. "Minor sprain" is a bit of a red herring, as a "sprain" essentially means some damage to a ligament or tendon - minor is just a few fibres, moderate is a partial tear, and major is a rupture (which you know all about if you've had ACL surgery.) If the orthopod you saw didn't specify the nature of the sprain, it's really hard to know what you should be doing.
I think the best advice I can offer - given that I'm not a medical professional and have no idea what's really going on with your knee - is to be super cautious when you start exercising again. Swimming is generally a fairly safe option, but only if you stick to flutter kicks - frog/whip kicks can put quite a bit of strain on the knee. Closed chain exercises are much safer than open. Cycling or stationary biking is usually pretty safe as well. Take a look at the ACL rehab exercises over on the info hub, and maybe start with the early stage exercises (which are all closed chain). If you get any kind of reaction from your knee, or feel any instability, get it re-evaluated right away.
It's great that you had no abnormal movements on the Lachman test, but with limited access to an OS or PT it's really much better to be safe than sorry. Start cautiously, and then build up gradually if everything seems good. Definitely not worth chancing your knee given all the work that goes into recovering from an ACL reconstruction.