Its conceivable that this can cause your email to be detected as spam, but HIGHLY, HIGHLY unlikely - for a number of reasons.
The most compelling reason is that most of these blacklists are used at the MTA level (ie ISP to ISP) to check that the email is being sent through a mail server not known for sending spam. You pass this check.
The second reason is that any mail administrator of any worth knows and understands that end user IP's get into these blacklists - often through no fault of the person using the IP. (For example, worms generally do direct from host sending which is blocked by these filters, and ISP's know IP's are dynamically assigned and subject to change).
Another thing to point out is that it is entirely possible your ISP is not bad (I don't know them of-course), and that the "blacklist" your IP is on is not actually a blacklist, rather a list your ISP has made known - or someone has worked out - is part of a dynamic pool and should not be used to send mail directly. Again, this is well known and accepted - so email originating from this IP DIRECTLY is blocked.
yet another reason ISP's won't care about your IP in the header is because its there to assist in tracking spam - which means the ISP whose mail server you are using it cares to add that header. This probably also means they are doing some spam checks on email passing through there system and are probably not an open relay.
Yet another reason not to worry is because these headers are arbitrarily added to emails - it is not uncommon for there to be a chain of them. Generally Spam programs only care about the last one, because all the others can be faked relatively trivially, and are used for admin purposes.
The last reason is that any even half decent spam filtering system will not blacklist simply on IP address - rather it considers a number of factors - of which the IP address may be one, weighs them, and then classifies it.
If, Notwithstanding my answer you want to "do something" besides switching ISP, running a VPN from your PC will change the IP address associated with your emails. But really, this is not neccessary.
[ BTW, I have been in the ISP industry for quite a long time, have run a mail server for a financial service based company, implemented spam filters and mail servers, so I have a fair idea of what I'm talking about ].