The best thing to do might be to get your windows replaced. I got some quotes about 6 months ago, and it was cheaper than I thought it would be. Of course, the prices did vary from company to company, so you would want to get at least 3 quotes. Just to give you an idea, it would be about $2500.00 for me to get 6 windows replaced.
Keep in mind that moister around the windows can lead to bigger problems. First, it could cause damage to the wood beyond the window area. That could lead to a bigger repair job. Also, damp wood attracts termites.
If you don't have the money to spend right now, then caulk and paint will get you by for a while. (That is what we are doing until we are ready to spend the $$$ for new windows.) I wonder about replacing wood at this time. It does seem like a waist to go through all that trouble without getting new windows.
Water is probably getting in around the window frames (where they meet with the house). Sealing them with caulk and paint should keep the water out. Of course, if the painter wants to replace just the window trim, then that could be helpful and pretty cheap.
It won't hurt to get some quotes and compare prices. Just keep in mind that the people who come to your house to give you quotes are sales people. Don't let them pressure you into spending too much.
The painter should be fine to replace simple widow trim. But, how nice are your windows? Are they worth saving? Can you afford new windows, and maybe other repairs to your house from water damage? Have I caused you more trouble than help?
In short, some new trim, caulk, and paint should keep the water from coming in around the frame of your windows. If your windows are otherwise nice, then they are worth saving. If they aren't, then you might want to see what it would cost to get new windows compared to the repairs. Good luck.