It's not standard to medicate for autism, FYI. The standard recommendation is therapy (Applied Behavioral Analysis, occupational therapy, and speech therapy are most common). One benefit of a diagnosis is that often your insurance company will cover more therapy.
The right next step is to get an actual diagnosis, in my opinion. You might be off-base in your suspicions, or it may turn out that your child is more affected than you suspect.
After diagnosis? There are no drugs specifically indicated for treating ASD. You might find people on the spectrum getting prescribed ADHD meds, say, but I understand that's more of the exception nowadays.
The right next step is to get an actual diagnosis, in my opinion. You might be off-base in your suspicions, or it may turn out that your child is more affected than you suspect.