I don't know how you avoid sex, and I am not sure you need to if it will make him suspicious (I know a lot of people won't agree with that advice but at this point, keeping everything "normal" while you gather evidence is crucial). You should go to the GUM clinic immediately and get tested (but for heavens sake make sure he doesn't know that you have done so). Even if you catch something (god forbid) there's really not much that isn't curable.
Keep everything as normal as you can and be sweet and computer stupid. Don't let him see you check his phone. When you do check his computer delete links only from the last hour (after you have finished checking).
When you find anything, take a screenshot and print it off (don't save the image on the computer!!).
Does the mobile bill come to the house? Does it show numbers dialled and received? Check your bank accounts (and his if they are separate) and look for large unexplained cash withdrawals. DO NOT ask him anything about anything at this point!!!
Check his bathroom for condoms. If you have used them with him previously count them and write it down somewhere and see if any disappear.
Check the glove box of his car and under the seats, etc for condoms as well.
If you can afford it you can also put a GPS tracker in his car - it shows exactly where he goes.
Some people will say if you have to do all this there is no trust and you should just leave now and not resort to snooping - but it sounds like you aren't going anywhere without proof, so get it.
The last thing I will say, and I do so with kindness, is that even with busy schedules there is always time for sex. Couples make time. In two months there are many many hours or half hours with opportunity even if you are running the United States of America - people make time for what is important to them. Where there's a will there's a way. Two months is a hell of a long time at your age for no sex, and as you talk about sex as a "gift" and him "pestering", it sounds like it may be you that isn't interested in sex. Which is fine!!! If you aren't you aren't! But that doesn't justify him hiring whores and surely is a deal breaker isn't it? Or is it him that isn't interested? Have you had conversations about sex? You can tell us anything and we will try to help - you are 100% anonymous and so are we, so let it all out sweetheart. xx